A258359 Sum over all partitions lambda of n into 4 distinct parts of Product_{i:lambda} prime(i).

210, 330, 852, 1826, 4207, 6595, 13548, 21479, 38905, 59000, 95953, 142843, 231431, 324152, 487361, 683227, 1003028, 1347337, 1907811, 2541970, 3526314, 4597020, 6194948, 7969172, 10618000, 13401580, 17424498, 21875750, 28102737, 34685941, 43856482, 53791587

Offset: 10

Author

Alois P. Heinz, May 27 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..1000

Crossrefs

Column k=4 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, 5), polynom)
    end:
a:= n-> coeff(g(n$2), x, 4):
seq(a(n), n=10..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, 4];
a /@ Range[10, 60] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)