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%I #6 Oct 25 2022 11:38:52
%S 1,0,1,0,2,0,2,0,1,0,3,0,3,0,2,0,4,0,4,0,2,0,4,0,4,0,1,0,4,0,5,0,3,0,
%T 4,0,5,0,3,0,6,0,6,0,2,0,6,0,4,0,4,0,6,0,6,0,4,0,7,0,7,0,2,0,6,0,8,0,
%U 4,0,8,0,8,0,4,0,6,0,8,0,1,0,9,0,8,0,4
%N Replace prime(k) with A000720(k) in the prime factorization of n.
%e We have 91 = prime(4) * prime(6), so a(91) = pi(4) * pi(6) = 6.
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Times@@PrimePi/@primeMS[n],{n,100}]
%Y Other multiplicative sequences: A003961, A045966, A064988, A064989, A357983.
%Y The version for p instead of pi is A299200, horz A357977, strict A357982.
%Y The version for nu is A355741.
%Y The version for bigomega is A355742.
%Y The horizontal version is A357980.
%Y A000040 lists the prime numbers.
%Y A000720 is PrimePi.
%Y A056239 adds up prime indices, row-sums of A112798.
%Y Cf. A033879, A033880, A063834, A066207, A076610, A296150, A357975.
%K nonn,mult
%O 1,5
%A _Gus Wiseman_, Oct 25 2022
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