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A341143
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Number of partitions of n into 6 distinct prime powers (including 1).
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8
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1, 1, 1, 1, 3, 3, 5, 5, 7, 8, 10, 10, 16, 16, 20, 22, 28, 27, 35, 36, 44, 47, 56, 57, 70, 72, 81, 89, 102, 105, 122, 128, 140, 151, 167, 175, 197, 208, 223, 241, 259, 272, 296, 316, 331, 359, 378, 400, 423, 452, 468, 507, 525, 556, 580, 619, 631, 684, 701, 748
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OFFSET
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22,5
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LINKS
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MAPLE
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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, 6):
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MATHEMATICA
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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, 6];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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