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A341074
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Number of partitions of n into 5 distinct squarefree parts.
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6
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1, 1, 1, 0, 2, 3, 3, 3, 5, 8, 9, 8, 11, 15, 16, 16, 22, 27, 30, 31, 38, 46, 48, 49, 57, 72, 73, 76, 90, 107, 109, 112, 128, 151, 156, 160, 182, 214, 220, 224, 250, 290, 297, 306, 335, 387, 399, 409, 442, 503, 517, 529, 572, 641, 660, 676, 726, 809, 829, 846, 903
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OFFSET
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17,5
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LINKS
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MAPLE
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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`(numtheory[issqrfree](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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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[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 5];
Table[Count[IntegerPartitions[n, {5}], _?(Length[Union[#]]==5&&AllTrue[#, SquareFreeQ]&)], {n, 17, 80}] (* Harvey P. Dale, Sep 05 2023 *)
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CROSSREFS
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Cf. A005117, A008966, A098236, A307835, A308840, A341065, A341073, A341075, A341095, A341096, A341097, A341098.
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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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