A341147 Number of partitions of n into 10 distinct prime powers (including 1).

1, 0, 0, 1, 1, 1, 2, 1, 3, 3, 3, 4, 7, 5, 9, 10, 12, 10, 17, 17, 23, 24, 29, 32, 44, 40, 53, 57, 71, 71, 91, 90, 113, 117, 141, 148, 181, 181, 217, 231, 268, 276, 327, 340, 397, 412, 472, 493, 571, 590, 671, 710, 794, 831, 934, 981, 1094, 1150, 1271, 1345, 1484, 1556, 1706

Offset

63,7

Links

Table of n, a(n) for n=63..125.

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-1), t-1), 0)))
    end:
a:= n-> b(n$2, 10):
seq(a(n), n=63..125);  # 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 - 1], t - 1], 0]]];
a[n_] := b[n, n, 10];
Table[a[n], {n, 63, 125}] (* Jean-François Alcover, Mar 01 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000961, A010055, A341131, A341132, A341139, A341140, A341141, A341142, A341143, A341144, A341145, A341146.

Sequence in context: A360033 A303974 A153868 * A325335 A262952 A245367

Adjacent sequences: A341144 A341145 A341146 * A341148 A341149 A341150

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved