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A341144
Number of partitions of n into 7 distinct prime powers (including 1).
8
1, 1, 1, 1, 2, 3, 3, 4, 6, 8, 8, 10, 12, 15, 16, 22, 23, 29, 30, 37, 40, 50, 50, 63, 68, 79, 81, 99, 101, 121, 127, 147, 153, 182, 182, 214, 224, 253, 262, 304, 309, 351, 365, 405, 421, 477, 485, 541, 563, 614, 634, 706, 719, 791, 823, 888, 919, 1006, 1029, 1115, 1164
OFFSET
30,5
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, 7):
seq(a(n), n=30..90); # 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, 7];
Table[a[n], {n, 30, 90}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 05 2021
STATUS
approved