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A300715
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Number of compositions (ordered partitions) of n into squares that do not divide n.
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1
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 4, 3, 0, 0, 7, 6, 0, 0, 14, 10, 4, 0, 22, 20, 10, 0, 32, 39, 20, 0, 49, 70, 42, 0, 12, 116, 88, 0, 128, 156, 174, 11, 207, 3, 320, 0, 333, 551, 575, 0, 555, 914, 0, 0, 959, 1502, 1829, 44, 1691, 2486, 3192, 0, 3000, 4172, 4005
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OFFSET
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0,14
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LINKS
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EXAMPLE
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a(21) = 4 because we have [9, 4, 4, 4], [4, 9, 4, 4], [4, 4, 9, 4] and [4, 4, 4, 9].
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MAPLE
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a:= proc(m) option remember; local b; b:= proc(n) option
remember; `if`(n=0, 1, add((s->`if`(s>n or irem(m, s)
=0, 0, b(n-s)))(j^2), j=2..isqrt(n))) end; b(m)
end:
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MATHEMATICA
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Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && IntegerQ[k^(1/2)]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 75}]
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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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