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A341125
Number of partitions of n into 7 prime powers (including 1).
9
1, 1, 2, 3, 5, 6, 10, 13, 18, 22, 30, 35, 47, 54, 68, 78, 97, 107, 132, 146, 173, 190, 225, 242, 285, 305, 352, 377, 434, 456, 525, 553, 627, 659, 748, 778, 881, 916, 1028, 1068, 1197, 1232, 1381, 1421, 1578, 1619, 1801, 1837, 2041, 2079, 2296, 2337, 2583, 2613
OFFSET
7,3
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, 7):
seq(a(n), n=7..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, 7];
Table[a[n], {n, 7, 60}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 05 2021
STATUS
approved