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A294333
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Number of partitions of n into cubes dividing n.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 3, 1, 8, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 11, 4, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 14, 1
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OFFSET
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0,9
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LINKS
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FORMULA
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a(n) = 1 if n is a cubefree.
a(n) = 2 if n is a cube of prime.
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EXAMPLE
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a(8) = 2 because 8 has 4 divisors {1, 2, 4, 8} among which 2 are cubes {1, 8} therefore we have [8] and [1, 1, 1, 1, 1, 1, 1, 1].
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MATHEMATICA
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Table[SeriesCoefficient[Product[1/(1 - Boole[Mod[n, k] == 0 && IntegerQ[k^(1/3)]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 105}]
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PROG
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(PARI)
cubes_dividing(n) = select(d -> ispower(d, 3), divisors(n));
partitions_into(n, parts, from=1) = if(!n, 1, my(k = #parts, s=0); for(i=from, k, if(parts[i]<=n, s += partitions_into(n-parts[i], parts, i))); (s));
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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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