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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).

%I A094756 #19 Dec 19 2018 15:05:23
%S A094756 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 A094756 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 A094756 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 A094756 a(n) = least k>1 such that (1+2+3+...+k) divides (1^n + 2^n + 3^n + ... + k^n).
%H A094756 Antti Karttunen, <a href="/A094756/b094756.txt">Table of n, a(n) for n = 1..20000</a>
%H A094756 Antti Karttunen, <a href="/A094756/a094756.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A094756 Formulae from _Don Reble_: If N is not divisible by 2, a(N) = 2.
%F A094756 Otherwise, if N is not divisible by 4, a(N) = 4.
%F A094756 Otherwise, if N is not divisible by 12, a(N) = 7.
%F A094756 Otherwise, if N is not divisible by 48, a(N) = 16.
%F A094756 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 A094756 Otherwise, if N is not divisible by 720, a(N) = 37.
%F A094756 Otherwise, if N is not divisible by 11 nor 23, a(N) = 46.
%F A094756 Otherwise, if N is not divisible by 77, a(N) = 58.
%F A094756 Otherwise, if N is not divisible by 13 nor 53, a(N) = 106.
%F A094756 Otherwise, if N is not divisible by 13, a(N) = 157.
%F A094756 Otherwise, if N is not divisible by 41 nor 83, a(N) = 166. ...
%F A094756 That works for N < 29549520 or so. But it is unlikely that any finite description of that kind is complete.
%t A094756 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 A094756 (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 A094756 Cf. A094755, A095366.
%K A094756 nonn
%O A094756 1,1
%A A094756 _Amarnath Murthy_, May 29 2004
%E A094756 Edited and extended by _Don Reble_ and _Robert G. Wilson v_, Jun 02 2004