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%I #18 Mar 07 2024 09:04:50
%S 1,3,3,167,11,489,43,282407,171,110865,683,3710553451913,2731,
%T 27323481,10923,1293248801687,43691,6910715937,174763,
%U 2983746256027727,699051,1762357129833,2796203,734630194457006903941170593,11184811,450614156030769,44739243
%N Least integer value of (1 + 2^n + 3^n + ... + k^n)/(1 + 2 + 3 + ... + k), k > 1.
%H Alois P. Heinz, <a href="/A094755/b094755.txt">Table of n, a(n) for n = 1..719</a>
%e a(4) = (1^4 + 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 7^4)/(1+2+3+4+5+6+7) = 4676/28 = 167, k = 7.
%e a(5) = (1^5 + 2^5)/(1 + 2) = 11, k = 2.
%p a:= proc(n) option remember; local k,r,s,t; s, t:=1$2;
%p for k from 2 do s, t:= s+k, t+k^n;
%p if irem(t, s, 'r')=0 then return r fi
%p od:
%p end:
%p seq(a(n), n=1..28); # _Alois P. Heinz_, Mar 07 2024
%t f[n_] := Block[{k = 2}, While[s = 2Sum[i^n, {i, k}]/(k(k + 1)); !IntegerQ[s], k++ ]; s]; Table[ f[n], {n, 25}] (* _Robert G. Wilson v_, Jun 02 2004 *)
%Y Cf. A000217, A094756.
%K nonn
%O 1,2
%A _Amarnath Murthy_, May 29 2004
%E Edited and extended by _Robert G. Wilson v_, Jun 02 2004
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