A341131 Number of partitions of n into 10 prime powers (including 1).

1, 1, 2, 3, 5, 6, 10, 13, 19, 24, 34, 41, 56, 67, 87, 105, 134, 156, 196, 228, 278, 320, 387, 439, 526, 593, 698, 783, 915, 1014, 1179, 1304, 1497, 1648, 1884, 2058, 2342, 2551, 2882, 3130, 3524, 3802, 4266, 4595, 5125, 5504, 6124, 6548, 7263, 7750, 8558

Offset: 10

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

• nonn

Crossrefs

Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341124, A341125, A341126, A341127.

Programs

Maple

q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(q(i), b(n-i, min(n-i, i), t-1), 0)))
    end:
a:= n-> b(n$2, 10):
seq(a(n), n=10..60);  # Alois P. Heinz, Feb 05 2021

Mathematica

q[n_] := q[n] = Length[FactorInteger[n]] < 2;
b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
     If[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 10];
Table[a[n], {n, 10, 60}] (* Jean-François Alcover, Feb 27 2022, after Alois P. Heinz *)