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A341146
Number of partitions of n into 9 distinct prime powers (including 1).
2
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
50,6
LINKS
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 *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 05 2021
STATUS
approved