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A341145
Number of partitions of n into 8 distinct prime powers (including 1).
8
1, 0, 1, 1, 2, 1, 2, 3, 5, 5, 6, 7, 10, 10, 13, 16, 19, 21, 26, 30, 34, 37, 44, 52, 58, 66, 73, 85, 94, 106, 115, 136, 146, 165, 178, 204, 215, 248, 263, 298, 318, 356, 372, 426, 443, 494, 520, 585, 603, 681, 702, 781, 815, 906, 929, 1044, 1071, 1178, 1223
OFFSET
39,5
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, 8):
seq(a(n), n=39..97); # 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, 8];
Table[a[n], {n, 39, 97}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 05 2021
STATUS
approved