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A341131
Number of partitions of n into 10 prime powers (including 1).
2
1, 1, 2, 3, 5, 6, 10, 13, 19, 24, 34, 41, 56, 67, 87, 105, 134, 156, 196, 228, 278, 320, 387, 439, 526, 593, 698, 783, 915, 1014, 1179, 1304, 1497, 1648, 1884, 2058, 2342, 2551, 2882, 3130, 3524, 3802, 4266, 4595, 5125, 5504, 6124, 6548, 7263, 7750, 8558
OFFSET
10,3
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, 10):
seq(a(n), n=10..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, 10];
Table[a[n], {n, 10, 60}] (* Jean-François Alcover, Feb 27 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 05 2021
STATUS
approved