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A258362 Sum over all partitions lambda of n into 7 distinct parts of Product_{i:lambda} prime(i).

%I A258362 #4 May 27 2015 17:29:27
%S A258362 510510,570570,1436820,2655870,5532330,9757518,19659886,34710965,
%T A258362 58356321,96541978,161476211,256683013,419693431,647984259,1021626403,
%U A258362 1536889595,2332063802,3443800806,5133970767,7443724123,10827942578,15520714599,22052126419,30994058608
%N A258362 Sum over all partitions lambda of n into 7 distinct parts of Product_{i:lambda} prime(i).
%H A258362 Alois P. Heinz, <a href="/A258362/b258362.txt">Table of n, a(n) for n = 28..1000</a>
%p A258362 g:= proc(n, i) option remember; convert(series(`if`(n=0, 1,
%p A258362       `if`(i<1, 0, add(g(n-i*j, i-1)*(ithprime(i)*x)^j
%p A258362       , j=0..min(1, n/i)))), x, 8), polynom)
%p A258362     end:
%p A258362 a:= n-> coeff(g(n$2), x, 7):
%p A258362 seq(a(n), n=28..60);
%Y A258362 Column k=7 of A258323.
%Y A258362 Cf. A000040.
%K A258362 nonn
%O A258362 28,1
%A A258362 _Alois P. Heinz_, May 27 2015