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A341127
Number of partitions of n into 9 prime powers (including 1).
9
1, 1, 2, 3, 5, 6, 10, 13, 19, 24, 33, 40, 54, 64, 83, 99, 125, 144, 180, 206, 250, 284, 341, 383, 455, 506, 593, 656, 762, 835, 965, 1054, 1206, 1309, 1491, 1610, 1825, 1964, 2213, 2374, 2664, 2843, 3179, 3387, 3769, 3998, 4440, 4695, 5194, 5480, 6043, 6357
OFFSET
9,3
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, 9):
seq(a(n), n=9..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, 9];
Table[a[n], {n, 9, 60}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 05 2021
STATUS
approved