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A011772 Smallest number m such that m(m+1)/2 is divisible by n. 19
1, 3, 2, 7, 4, 3, 6, 15, 8, 4, 10, 8, 12, 7, 5, 31, 16, 8, 18, 15, 6, 11, 22, 15, 24, 12, 26, 7, 28, 15, 30, 63, 11, 16, 14, 8, 36, 19, 12, 15, 40, 20, 42, 32, 9, 23, 46, 32, 48, 24, 17, 39, 52, 27, 10, 48, 18, 28, 58, 15, 60, 31, 27, 127, 25, 11, 66, 16, 23, 20, 70, 63, 72, 36, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(2^k) = 2^(k+1)-1; a(m)=m-1 and for odd prime powers m. - Reinhard Zumkeller, Feb 26 2003

REFERENCES

C. Ashbacher, The Pseudo-Smarandache Function and the Classical Functions of Number Theory, Smarandache Notions Journal, Vol. 9, No. 1-2, 1998, 79-82.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Jason Earls, The Smarandache sum of composites between factors function, in Smarandache Notions Journal (2004), Vol. 14.1, page 246.

K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996, 50 pages. See p. 35.

K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996, 50 pages. [Cached copy] See p. 35.

Eric Weisstein's World of Mathematics, Pseudosmarandache Function

FORMULA

a(n) <= 2n-1 for all numbers n; a(n) <= n-1 for odd n. - Stefan Steinerberger, Apr 03 2006

a(n) >= (sqrt(8n+1)-1)/2 for all n. - Charles R Greathouse IV, Jun 25 2017

MATHEMATICA

Table[m := 1; While[Not[IntegerQ[(m*(m + 1))/(2n)]], m++ ]; m, {n, 1, 90}] (* Stefan Steinerberger, Apr 03 2006 *)

(Sqrt[1+8#]-1)/2&/@Flatten[With[{r=Accumulate[Range[300]]}, Table[ Select[r, Divisible[#, n]&, 1], {n, 80}]]] (* Harvey P. Dale, Feb 05 2012 *)

PROG

(Haskell)

import Data.List (findIndex)

import Data.Maybe (fromJust)

a011772 n = (+ 1) $ fromJust $

   findIndex ((== 0) . (`mod` n)) $ tail a000217_list

-- Reinhard Zumkeller, Mar 23 2013

(PARI) a(n)=if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))) \\ Charles R Greathouse IV, Jun 25 2017

CROSSREFS

A066561(n)=A000217(a(n)).

Cf. A080982.

Sequence in context: A318457 A198501 A230072 * A060451 A220291 A129187

Adjacent sequences:  A011769 A011770 A011771 * A011773 A011774 A011775

KEYWORD

nonn,easy,nice

AUTHOR

Kenichiro Kashihara (Univxiq(AT)aol.com)

EXTENSIONS

More terms from Stefan Steinerberger, Apr 03 2006

STATUS

approved

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Last modified May 20 02:44 EDT 2019. Contains 323411 sequences. (Running on oeis4.)