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

30, 42, 136, 293, 551, 892, 1765, 2570, 4273, 6747, 9770, 13958, 21206, 28280, 39702, 54913, 72227, 94682, 127095, 160046, 206119, 263581, 327790, 406354, 512372, 616764, 754412, 921169, 1100165, 1314196, 1584835, 1854384, 2191013, 2590565, 3006512, 3495086

Offset: 6

Author

Alois P. Heinz, May 27 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1000

Crossrefs

Column k=3 of A258323.

Cf. A000040.

Programs

Maple

g:= proc(n, i) option remember; convert(series(`if`(n=0, 1,
      `if`(i<1, 0, add(g(n-i*j, i-1)*(ithprime(i)*x)^j
      , j=0..min(1, n/i)))), x, 4), polynom)
    end:
a:= n-> coeff(g(n$2), x, 3):
seq(a(n), n=6..60);

Mathematica

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]}]]];
a[n_] := Coefficient[g[n, n], x, 3];
a /@ Range[6, 60] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)