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A341142
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Number of partitions of n into 5 distinct prime powers (including 1).
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9
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1, 0, 1, 2, 3, 3, 5, 5, 7, 8, 10, 12, 15, 15, 18, 21, 23, 26, 31, 33, 36, 41, 43, 48, 52, 58, 62, 72, 72, 82, 85, 95, 97, 112, 112, 125, 127, 142, 142, 161, 159, 181, 180, 200, 196, 222, 217, 243, 239, 269, 261, 291, 284, 316, 308, 341, 332, 370, 358, 394, 381, 427, 414, 456
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OFFSET
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15,4
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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, 5):
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MATHEMATICA
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q[n_] := q[n] = PrimeNu[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, 5];
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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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