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A323519
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a(n) is the number of ways to fill a square matrix with the multiset of prime factors of n, if the number of prime factors (counted with multiplicity) is a perfect square, and a(n) = 0 otherwise.
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5
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1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 4, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 6, 1, 0, 0, 4, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 4, 0, 0, 1, 12, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 12, 0, 0
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OFFSET
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1,24
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LINKS
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FORMULA
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If A001222(n) is a perfect square, then a(n) = A008480(n). Otherwise, a(n) = 0.
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EXAMPLE
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The a(60) = 12 matrices:
[2 2] [2 2] [2 3] [2 3] [2 5] [2 5] [3 2] [3 2] [3 5] [5 2] [5 2] [5 3]
[3 5] [5 3] [2 5] [5 2] [2 3] [3 2] [2 5] [5 2] [2 2] [2 3] [3 2] [2 2]
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[IntegerQ[Sqrt[PrimeOmega[n]]], Length[Permutations[primeMS[n]]], 0], {n, 100}]
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CROSSREFS
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Cf. A000290, A008480, A026478, A056239, A089299, A103198, A112798, A120732, A323433, A323525, A323531.
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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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