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A258358 Sum over all partitions lambda of n into 3 distinct parts of Product_{i:lambda} prime(i).

%I A258358 #9 Dec 11 2020 07:28:35
%S A258358 30,42,136,293,551,892,1765,2570,4273,6747,9770,13958,21206,28280,
%T A258358 39702,54913,72227,94682,127095,160046,206119,263581,327790,406354,
%U A258358 512372,616764,754412,921169,1100165,1314196,1584835,1854384,2191013,2590565,3006512,3495086
%N A258358 Sum over all partitions lambda of n into 3 distinct parts of Product_{i:lambda} prime(i).
%H A258358 Alois P. Heinz, <a href="/A258358/b258358.txt">Table of n, a(n) for n = 6..1000</a>
%p A258358 g:= proc(n, i) option remember; convert(series(`if`(n=0, 1,
%p A258358       `if`(i<1, 0, add(g(n-i*j, i-1)*(ithprime(i)*x)^j
%p A258358       , j=0..min(1, n/i)))), x, 4), polynom)
%p A258358     end:
%p A258358 a:= n-> coeff(g(n$2), x, 3):
%p A258358 seq(a(n), n=6..60);
%t A258358 g[n_, i_] := g[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[g[n - i j, i - 1] (Prime[i] x)^j, {j, 0, Min[1, n/i]}]]];
%t A258358 a[n_] := Coefficient[g[n, n], x, 3];
%t A258358 a /@ Range[6, 60] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y A258358 Column k=3 of A258323.
%Y A258358 Cf. A000040.
%K A258358 nonn
%O A258358 6,1
%A A258358 _Alois P. Heinz_, May 27 2015