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%I #9 Mar 15 2015 20:27:27
%S 3,30,17,248,515,49682
%N Smallest number k>1 such that Sum_{i=1..k} Prime[i]^n divides Product_{i=1..k} Prime[i]^n.
%C a(7)>991430. - _Robert G. Wilson v_, Mar 02 2007
%e a(1) = 3 because 2 + 3 + 5 = 10 divides 2*3*5 = 30 but 2 + 3 = 5 does not divide 2*3 = 6.
%t f[n_] := Block[{k = 2, p = 2, s = 2^n}, While[p = p*Prime@ k; s = s + Prime@ k^n; PowerMod[p, n, s] != 0, k++ ]; k]; Do[ Print@ f@n, {n, 10}] (* _Robert G. Wilson v_ *)
%Y Cf. A051838 = Sum of first n primes divides product of first n primes. Cf. A125314 = Smallest number k>1 such that Sum_{i=1..k} i^n divides Product_{i=1..k} i^n. Cf. A007504, A002110, A024450, A098999, A122102, A122103.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Feb 24 2007
%E a(6) from _Robert G. Wilson v_, Mar 02 2007