A341124 Number of partitions of n into 6 prime powers (including 1).

1, 1, 2, 3, 5, 6, 10, 12, 17, 20, 27, 31, 41, 45, 56, 63, 77, 83, 101, 108, 128, 136, 160, 168, 196, 204, 236, 245, 281, 288, 331, 340, 387, 395, 450, 457, 519, 525, 594, 598, 677, 678, 763, 764, 855, 851, 957, 949, 1062, 1053, 1177, 1161, 1300, 1276, 1425, 1403, 1564

Offset

6,3

Links

Table of n, a(n) for n=6..62.

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, 6):
seq(a(n), n=6..62);  # 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, 6];
Table[a[n], {n, 6, 62}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

Crossrefs

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

Sequence in context: A191173 A240026 A213212 * A008627 A130900 A007211

Adjacent sequences: A341121 A341122 A341123 * A341125 A341126 A341127

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved