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

Author

Amarnath Murthy, May 29 2004

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A094755, A095366.

Programs

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 *)

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

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.

Extensions

Edited and extended by Don Reble and Robert G. Wilson v, Jun 02 2004