A341126 Number of partitions of n into 8 prime powers (including 1).

1, 1, 2, 3, 5, 6, 10, 13, 19, 23, 32, 38, 51, 60, 77, 90, 113, 128, 158, 179, 215, 240, 287, 316, 373, 409, 475, 517, 599, 645, 741, 799, 908, 971, 1104, 1173, 1326, 1408, 1580, 1670, 1874, 1967, 2198, 2310, 2563, 2680, 2976, 3097, 3426, 3566, 3926, 4070, 4485

Offset

8,3

Links

Table of n, a(n) for n=8..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, 8):
seq(a(n), n=8..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, 8];
Table[a[n], {n, 8, 60}] (* Jean-François Alcover, Feb 22 2022, after _Alois P. Heinz *)

Crossrefs

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

Sequence in context: A341125 A035953 A195054 * A341127 A087750 A341131

Adjacent sequences: A341123 A341124 A341125 * A341127 A341128 A341129

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved