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%I #7 Oct 27 2022 10:13:30
%S 1,0,0,1,0,0,0,0,1,0,0,2,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,0,0,
%T 0,1,0,0,0,2,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,1,0,0,0,0,
%U 0,2,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,0
%N Number of divisors of n with the same sum of prime indices as their quotient. Central column of A321144, taking gaps as 0's.
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e The a(3600) = 5 divisors, their prime indices, and the prime indices of their quotients:
%e 45: {2,2,3} * {1,1,1,1,3}
%e 50: {1,3,3} * {1,1,1,2,2}
%e 60: {1,1,2,3} * {1,1,2,3}
%e 72: {1,1,1,2,2} * {1,3,3}
%e 80: {1,1,1,1,3} * {2,2,3}
%t sumprix[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>k*PrimePi[p]]];
%t Table[Length[Select[Divisors[n],sumprix[#]==sumprix[n]/2&]],{n,100}]
%Y Positions of nonzero terms are A357976, counted by A002219.
%Y A001222 counts prime factors, distinct A001221.
%Y A056239 adds up prime indices, row sums of A112798.
%Y Cf. A033879, A033880, A064914, A181819, A213074, A235130, A237258, A276107, A300061, A321144, A357975.
%K nonn
%O 1,12
%A _Gus Wiseman_, Oct 27 2022
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