a brief history of smarandache function

7/27/2019 A BRIEF HISTORY OF SMARANDACHE FUNCTION

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IUD' BIS'rORr OF rD ~ C D I't1NCTIOH ( I I I )

by Dr. Constantin Dumitrescu

ADDENDA (III) :

New References concerninig th is function (got by theedi tor ia l board a f t e r August 1, 1994):

{ See the previous two issues of the journal for the f i r s t andsecond par ts of th is ar t ic le }

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[95] The journal was indexed by the <Mathematical Reviews>,Ann Arbor, MI, 94c, March 1994, XXI:

[96] David E. Zi tare l l i , review of A br ief history of the<Smarandache Function> , in <HISTORIA MATHEMATlCA>,

Academic Press, Inc. , Harcourt Brace Co., San Diego,New York, Boston, London, Sydney, Tokyo: Vol. 21, No.1,

F e b ~ u a r y 1994, 102; '21.1.42;and in <BISTORIA MATHEMATlCA>, Vol. 21, No.2 , May 1994,229; #21.2.28, #21.2.29;

[97J Carol Moore, Arizona State University Library, Letter toC. Dumitrescu and V. Seleacu concerning the SmarandacheFunction Archives, April 20, 1994:

[98 J T. Yau, Teaching the Smarandache Function to theAmerican Competition Students , abstract , Department ofMathematics, University of Oregon, 1994;Letter from Richard M. Koch, 6/14/94:

[99] George Fernandez, Paradise Valley Community College, Aninequation concerning the Smarandache Function , to theInternat ional Congress of Mathematicians ( ICM 94 ),

Z ~ r i c h 3-11 August 1994;[100] George Mitin vArie,escu, Sydney, Austral ia , abstract in

Orizonturi Albastre / Poeti RomAni in Exil , CogitoPublishing Rouse, Oradea, 1993, 89-90;

[101] Paula Shanks, <Mathematical Reviews>, Letter to R.Muller, December 6, 1993;

[102] Harold W. Bil l ings , Director of General Libraries , TheUniversity of Texas a t Austin, The Florentin SmarandchePapers (1978-1994) Special Collection, Archives ofAmerican Mathematics, Center for American History, SRR2.109, TX 78713, t e l . (512) 495-4129, f ive l inear feet ;

[103] M. Andrei, C. Dumitrescu, V. Seleacu, L. TuTescu, St.Zanfir, Some remarks on the Smarandache Function , in<Bulletin of Pure and Applied Sciences>, Editor Prof. M.N. Gopalan, Indian Ins t i tu te of Technology, Bombay,India, Vol. 13E (No.2) , 1995:

[104] I . Rotaru, Cine este F10rentin Smaranciache 1 , prefacefor Fugit . . . jurnal de lag:ir , p. 5, Ed. Tempus,Bucharest, 1994:

[105] Geo Stroe, postface for Fugit . . . jurnal de lagar ,



cover IV, Ed. Tempus, Bucharest , 1994;[106] Pe te r Bundschuh, Koln, Auswertung der eingesandten

Losungen , in <Elemente der Mathematik>, Switzer land,Vol. 49, N o . 3 , 1994, 127-8;

[107] Gh. Tomozei, Func t ia Smarandache , pre face to <Exis timpotr iva mea>, pre-paradoxis t poetry by F. Smara-ndache,

Ed. Macarie, T a r g o v i ~ t e , 1994, pp. 5-9;a lso in <Li te ra toru l> , Bucharest , Nr. 42 (159), 14-21

October 1994, p.6 ;[108] Khal id Khan, London School o f Economics, Let te r to the

Edi t o r / The Smarandache funct ion , in <MathematicalSpectrum>, Vol. 27, N o . 1 , 1994/5, 20-1;

[109] Pal G r ~ n a s St jo rda l , Norway, Let t e r to the Edi tor /The Smarandache funct ion , in <Mathematical Spectrum>,Vol. 27, N o . 1 , 1994/5, 21;

[110] Khal id Khan, London School of Economics, Solut ion to

Problem 26.8, in <Mathematical Spectrum>, Vol. 27, No.1 ,1994/5, 22;

a lso solved by David Johansen and Pol ly Show, DameAllan ' s Gir l s ' School , Newcast le upon Tyne, U. K.;

[119] Jane Friedman, Smarandache in Reverse / so lu t ion to

problem B-740, in <The Fibonacci Quarter ly>, USA,November 1994, pp. 468-9;

[120] A. St iuparu , Problem H-490, in <The FibonacciQuar ter ly>, Vol. 32, N o . 5 , November 1994, p.473;

[121] Dumitru Ichim, Cronic i , in <Cuvantul RomAnesc>,

Hamilton, Ont-ario, Canada, Anul 20, N r ~ 221, November1994, p.12;

[122] Mihaly Bencze, Open Quest ion: QQ 6, in <Octogon>,

B r a ~ o v , Vol. 2, N o . 1 , Apri l 1994, p.34;[123] Pro R. Halleux, redac teur en chef , <Archives

In te rna t iona le s d 'H i s to i r e des Sciences>, Univers i te deLiege, Belgique, Let t re vers R. Muller , l e 14 novembre1994;

[124] Floren t in Gh. Smarandache, An I n f i n i t y o f UnsolvedProblems concern ing a Funct ion in t he Number Theory ,ab s t r ac t in <Proceedings of the In te rna t iona l Congress o f

Mathematicians>, Sect ion 3: Number Theory, Univers i ty o f

Berkeley, CA, USA, 1986;[125] F. Smarandache, Problem 7856, in <Gamma>, B r a ~ o v , Anul

X, No. 3-4 (31-31), February 1988, p.77;[126] Marian Mirescu, Catedra la Funct ie i Smarandache

(drawing), in <Abracadabra>, Sal inas , CA, December 1994,

p. 20;[127] A. D. Rachieru, A v a l a n ~ a Smarandache , in <Banatul>,

T i m i ~ o a r a , Nr. 4, 1994;[128] Gh. Suciu, Spre America - Via Is tambul , in <Minerva>,

B i s t r i t a - N ~ s ~ u d , Anul V, No. 39-40, p.10, October -November 1994;

[129] Ion Radu Z ~ g r e a n u , , Exis t impotr iva mea' , in

<Minerva>, B i s t r i t a - N ~ s ~ u d , Anul V, No. 39-40, p.10,

October - November 1994;[130] R. Muller , ed i to r o f Unsolved Problems r e l a t ed to

Smarandache Funct ion , Number Theory Publ. Co., Phoenix,

6



1993;reviewed in <Mathematical Reviews>, Ann Arbor, 94m: 11005,

11-06:[131] Gh. Stroe , Smarandache Funct ion , in <Tempus>,

Bucharest , Anu1 I I I . Nr. 2(5) , November 1994, p.4 ;

[132] Dr. Dumitru Acu, Univers i ty o f Sibiu , Func1;.iaSmarandache , in <Abracadabra>, Sal inas , CA, January

1995, No. 27, Anu1 I I I , p.20;[133] Lucian Tu1;.escu, func1;.ia Smarandache , in

<Abracadabra>, Sal inas , CA, January 1995, No. 27, AnulI I I , p.20;

[134] Constant in M. popa, Func1;.ia n , in <Abracadabra>,Sal inas , CA, January 1995, No. 27, Anul I I I , p.20;

[135J Prof . M. N. Gopalan, Edi tor of <Bul le t in o f PureApplied Sciences>, Bombay, India , Let te r to M. Andrei ,December 26, 1994;

[136J Dr. Pe te r L. Renz, Academic Press , Cambridge,Massachuset ts , Le t t e r to R. Muller, January 11, 1995;

[137] Charles Ashbacher, review of the Smarandache func t ion

Journal , in <Journal o f Recreat ional Mathematics>, USA,Vol. 26(2), pp. 138-9, 1994;

[138] N. J . A. Sloane, S. Plouffe , B. Salvy, TheEncyclopaedia o f In teger Sequences , Academic Press ,

1995, M0453 N 1 ~ 7 ;a l so onl ine : [email protected] ;

[139] Edi tors o f <Mathematical Reviews>, review o f t he bookUnsolved Problems r e l a t ed to Smarandache Funct ion by F.

Smarandache, 94m:11005;[140] Jean-Marie De Koninck, Quebec, review o f t he paper A

func t ion in t he number theory by F. Smarandache, in

<MathematicalReviews>, 94m:11007,

p.6940;[141] Jean-Marie De Koninck, Quebec, review of the paper Some

l i nea r equat ions involving a func t ion in the numbertheory o f F. Smarandache, in <Mathematical Reviews>,94m:11008, p.6940;

[142] Armel Mercier , review o f the paper An i n f i n i t y o funsolved problems concerning a func t ion in the numbertheory o f F. Smarandache, in <Mathematical Reviews>,

94m:11010, p.6940;[143]Armel Mercier , review o f the paper Solving problems by

us ing a funct ion in the mnumber theory o f F.Smarandache, in <Mathematical Reviews>, 94m:l lOll ,

p.6941;(144] I . M. Radu, Bucharest , Le t t e r to the Edi tor ( The

Smarandache funct ion ) , in <Mathematical Spectrum>,Shef f i e ld Univers i ty , UK Vol. 27, N o . 2 , p. 43, 1994/5:

[145] Paul Erdos, Hungarian Academy o f Sciences , Le t t e r to the

Edi to r (nThe Smarandache funct ion i n t e r a l i a ) , in

<Mathematical Spectrum>, Vol. 27, N o . 2 , pp. 43-4,1994/5;

[146] I . Soare, Un s c r i i t o r a l paradoxur i lor : F lorent in

Smarandache , 114 pages , Ed. Almarom Rm. VIlcea ,Romania, p . 67, 1994;

[147] Dr. C. Dumitrescu, Funct ia Smarandache , in <Foaie

8



M a t e m a t i c ~ > C h i ~ i n ~ u Republic of Moldova, Nr. 3, 1995,p . 43;

[148] A. Stuparu, D. W. Sharpe, Problem 1, in <FoaieMatematica>, Chisinau, Republic o f Moldova, Nr. 3, 1995,

p . 43;[149] Pedro Melendez, Problem 2, in <Foaie Matematica>,

Chisinau, Republic of Moldova, Nr. 3, 1995, p. 43;

[150] Ken Tauscher, Problem 3, in <Foaie Matematica>,

Chisinau, Republic of Moldova, Nr. 3, 1995, p. 43;[151] T. Yau, Problem 4, in <Foaie Matematica>, Chisinau,

Republic of Moldova, Nr. 3, 1995, p. 43;[152] T. Popescu, "Es te t i ca Paradoxismului , (see

In t roduc t ion) , 150 pp. , 1995;[153] N. J . A. Sloane & S. Plouffe , The Encyclopedia of

In t eger Sequences , Academic Press , San Diego, New York,Boston, London, Sydney, Tokyo, Toronto, 1995;a l so onl ine , email : [email protected] t .com(SUPERSEEKER by N. J . A. Sloane, S. Plouffe , B. Salvy,

ATT Bel l Labs, Murray Hi l l , NJ 07974, USA); presented

as :

and

and

SMARANDACHE NUMBERS :[M0453] ,

S(n) , for n = 1 2 3

SMARANDACHE QUOTIENTS : for each i n t ege r n > 0,f ind the smal les t k such t ha t nk i s a f ac to r ia l ;[MI669];

SMARANDACHE DOUBLE FACTORIALS : F(n) i s the

smal les t in tege r such t ha t F(n ) i s d iv i s ib l e byn; [A7922] in the e lec t ron ic vers ion.

a brief history of smarandache function

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