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A323519 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.

%I A323519 #11 Feb 23 2019 10:10:45
%S A323519 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,
%T A323519 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,
%U A323519 0,0,1,0,1,0,0,0,0,0,1,0,1,0,1,12,0,0
%N A323519 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.
%F A323519 If A001222(n) is a perfect square, then a(n) = A008480(n). Otherwise, a(n) = 0.
%e A323519 The a(60) = 12 matrices:
%e A323519   [2 2] [2 2] [2 3] [2 3] [2 5] [2 5] [3 2] [3 2] [3 5] [5 2] [5 2] [5 3]
%e A323519   [3 5] [5 3] [2 5] [5 2] [2 3] [3 2] [2 5] [5 2] [2 2] [2 3] [3 2] [2 2]
%t A323519 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A323519 Table[If[IntegerQ[Sqrt[PrimeOmega[n]]],Length[Permutations[primeMS[n]]],0],{n,100}]
%Y A323519 Positions of 0's are A323521.
%Y A323519 Positions of 1's are A323520.
%Y A323519 Cf. A000290, A008480, A026478, A056239, A089299, A103198, A112798, A120732, A323433, A323525, A323531.
%K A323519 nonn
%O A323519 1,24
%A A323519 _Gus Wiseman_, Jan 17 2019