A094756 - OEIS

%I #19 Dec 19 2018 15:05:23

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A094756/b094756.txt">Table of n, a(n) for n = 1..20000</a>

%H Antti Karttunen, <a href="/A094756/a094756.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%F Formulae from _Don Reble_: If N is not divisible by 2, a(N) = 2.

%F Otherwise, if N is not divisible by 4, a(N) = 4.

%F Otherwise, if N is not divisible by 12, a(N) = 7.

%F Otherwise, if N is not divisible by 48, a(N) = 16.

%F Otherwise, if N is not divisible by 240, a(N) = 22 or 31. (31 if N is divisible by 528=11*48; otherwise 22).

%F Otherwise, if N is not divisible by 720, a(N) = 37.

%F Otherwise, if N is not divisible by 11 nor 23, a(N) = 46.

%F Otherwise, if N is not divisible by 77, a(N) = 58.

%F Otherwise, if N is not divisible by 13 nor 53, a(N) = 106.

%F Otherwise, if N is not divisible by 13, a(N) = 157.

%F Otherwise, if N is not divisible by 41 nor 83, a(N) = 166. ...

%F That works for N < 29549520 or so. But it is unlikely that any finite description of that kind is complete.

%t 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 *)

%o (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

%Y Cf. A094755, A095366.

%K nonn

%O 1,1

%A _Amarnath Murthy_, May 29 2004

%E Edited and extended by _Don Reble_ and _Robert G. Wilson v_, Jun 02 2004