A341146 Number of partitions of n into 9 distinct prime powers (including 1).
1, 0, 1, 0, 1, 2, 2, 1, 4, 4, 5, 5, 8, 7, 11, 11, 16, 16, 21, 20, 30, 30, 36, 40, 51, 53, 63, 67, 82, 89, 105, 111, 133, 143, 163, 176, 203, 218, 246, 267, 301, 324, 357, 389, 431, 471, 512, 555, 607, 660, 710, 773, 835, 906, 969, 1057, 1124, 1224, 1298, 1407, 1494
Offset: 50
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 50..5000
Crossrefs
Programs
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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, 9): seq(a(n), n=50..110); # 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, 9]; Table[a[n], {n, 50, 110}] (* Jean-François Alcover, Feb 27 2022, after Alois P. Heinz *)