A094756 a(n) = least k>1 such that (1+2+3+...+k) divides (1^n + 2^n + 3^n + ... + k^n).

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

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

Cf. A094755, A095366.

Sequence in context: A177847 A296471 A021416 * A307667 A228367 A110925

Adjacent sequences: A094753 A094754 A094755 * A094757 A094758 A094759

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