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URL: https://oeis.org/A094756

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A094756
a(n) = least k>1 such that (1+2+3+...+k) divides (1^n + 2^n + 3^n + ... + k^n).
3
2, 4, 2, 7, 2, 4, 2, 7, 2, 4, 2, 16, 2, 4, 2, 7, 2, 4, 2, 7, 2, 4, 2, 16, 2, 4, 2, 7, 2, 4, 2, 7, 2, 4, 2, 16, 2, 4, 2, 7, 2, 4, 2, 7, 2, 4, 2, 22, 2, 4, 2, 7, 2, 4, 2, 7, 2, 4, 2, 16, 2, 4, 2, 7, 2, 4, 2, 7, 2, 4, 2, 16, 2, 4, 2, 7, 2, 4, 2, 7, 2, 4, 2, 16, 2, 4, 2, 7, 2, 4, 2, 7, 2, 4, 2, 22, 2, 4, 2, 7, 2, 4
OFFSET
1,1
FORMULA
Formulae from Don Reble: If N is not divisible by 2, a(N) = 2.
Otherwise, if N is not divisible by 4, a(N) = 4.
Otherwise, if N is not divisible by 12, a(N) = 7.
Otherwise, if N is not divisible by 48, a(N) = 16.
Otherwise, if N is not divisible by 240, a(N) = 22 or 31. (31 if N is divisible by 528=11*48; otherwise 22).
Otherwise, if N is not divisible by 720, a(N) = 37.
Otherwise, if N is not divisible by 11 nor 23, a(N) = 46.
Otherwise, if N is not divisible by 77, a(N) = 58.
Otherwise, if N is not divisible by 13 nor 53, a(N) = 106.
Otherwise, if N is not divisible by 13, a(N) = 157.
Otherwise, if N is not divisible by 41 nor 83, a(N) = 166. ...
That works for N < 29549520 or so. But it is unlikely that any finite description of that kind is complete.
MATHEMATICA
f[n_] := Block[{k = 2}, While[ !IntegerQ[ 2Sum[i^n, {i, k}]/(k(k + 1))], k++ ]; k]; Table[ f[n], {n, 50}] (* Robert G. Wilson v, Jun 02 2004 *)
PROG
(PARI) A094756(n) = { my(k=1, s1=1, s2=1); while(1, k++; s1 += k; s2 += (k^n); if(!(s2%s1), return(k))); }; \\ Antti Karttunen, Dec 19 2018
CROSSREFS
Sequence in context: A177847 A296471 A021416 * A307667 A228367 A110925
KEYWORD
nonn
AUTHOR
Amarnath Murthy, May 29 2004
EXTENSIONS
Edited and extended by Don Reble and Robert G. Wilson v, Jun 02 2004
STATUS
approved