A341123 Number of partitions of n into 5 prime powers (including 1).

1, 1, 2, 3, 5, 6, 9, 11, 15, 17, 23, 25, 32, 34, 42, 45, 55, 56, 68, 71, 83, 84, 100, 100, 117, 118, 136, 135, 158, 153, 179, 178, 204, 200, 234, 226, 261, 255, 291, 283, 327, 310, 357, 344, 390, 371, 430, 405, 466, 444, 505, 476, 550, 511, 589, 557, 634, 589, 684, 629

Offset

5,3

Links

Table of n, a(n) for n=5..64.

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, 5):
seq(a(n), n=5..64);  # 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, 5];
Table[a[n], {n, 5, 64}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

Crossrefs

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

Sequence in context: A239010 A104738 A319469 * A365877 A325863 A341868

Adjacent sequences: A341120 A341121 A341122 * A341124 A341125 A341126

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved