A341125 Number of partitions of n into 7 prime powers (including 1).

1, 1, 2, 3, 5, 6, 10, 13, 18, 22, 30, 35, 47, 54, 68, 78, 97, 107, 132, 146, 173, 190, 225, 242, 285, 305, 352, 377, 434, 456, 525, 553, 627, 659, 748, 778, 881, 916, 1028, 1068, 1197, 1232, 1381, 1421, 1578, 1619, 1801, 1837, 2041, 2079, 2296, 2337, 2583, 2613

Offset

7,3

Links

Table of n, a(n) for n=7..60.

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, 7):
seq(a(n), n=7..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, 7];
Table[a[n], {n, 7, 60}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

Crossrefs

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

Sequence in context: A202823 A013931 A018429 * A035953 A195054 A341126

Adjacent sequences: A341122 A341123 A341124 * A341126 A341127 A341128

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved