A341147 Number of partitions of n into 10 distinct prime powers (including 1).
1, 0, 0, 1, 1, 1, 2, 1, 3, 3, 3, 4, 7, 5, 9, 10, 12, 10, 17, 17, 23, 24, 29, 32, 44, 40, 53, 57, 71, 71, 91, 90, 113, 117, 141, 148, 181, 181, 217, 231, 268, 276, 327, 340, 397, 412, 472, 493, 571, 590, 671, 710, 794, 831, 934, 981, 1094, 1150, 1271, 1345, 1484, 1556, 1706
Offset: 63
Keywords
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, 10): seq(a(n), n=63..125); # 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, 10]; Table[a[n], {n, 63, 125}] (* Jean-François Alcover, Mar 01 2022, after Alois P. Heinz *)