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A294105
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Number of compositions (ordered partitions) of n into squares dividing n.
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3
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1, 1, 1, 1, 2, 1, 1, 1, 7, 2, 1, 1, 26, 1, 1, 1, 96, 1, 12, 1, 345, 1, 1, 1, 1252, 2, 1, 76, 4544, 1, 1, 1, 17473, 1, 1, 1, 127654, 1, 1, 1, 217286, 1, 1, 1, 788674, 2490, 1, 1, 3182706, 2, 28, 1, 10390321, 1, 14128, 1, 37713313, 1, 1, 1, 136886433, 1, 1, 80396, 579739960, 1, 1, 1, 1803399103, 1, 1
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OFFSET
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0,5
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LINKS
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EXAMPLE
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a(8) = 7 because 8 has 4 divisors {1, 2, 4, 8} among which 2 are squares {1, 4} therefore we have [4, 4], [4, 1, 1, 1, 1], [1, 4, 1, 1, 1], [1, 1, 4, 1, 1], [1, 1, 1, 4, 1], [1, 1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1, 1].
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MAPLE
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a:= proc(n) option remember; local b, l;
l, b:= select(issqr, numtheory[divisors](n)),
proc(m) option remember; `if`(m=0, 1,
add(`if`(j>m, 0, b(m-j)), j=l))
end; b(n)
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, 70}]
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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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