A258360 Sum over all partitions lambda of n into 5 distinct parts of Product_{i:lambda} prime(i).

2310, 2730, 7860, 15606, 35594, 67255, 120061, 201324, 364479, 592991, 1004771, 1530056, 2444073, 3691392, 5610179, 8334486, 12213775, 17529361, 25187765, 35345858, 49999364, 68516285, 94223007, 127478773, 172613052, 230362430, 305639795, 401637665, 527011287

Offset: 15

Author

Alois P. Heinz, May 27 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 15..1000

Crossrefs

Column k=5 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, 6), polynom)
    end:
a:= n-> coeff(g(n$2), x, 5):
seq(a(n), n=15..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, 5];
a /@ Range[15, 60] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)