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%I #8 Jan 29 2020 02:57:29
%S 0,0,0,0,0,1,0,0,1,2,0,1,0,3,0,0,0,0,0,2,1,4,0,1,2,5,1,3,0,1,0,0,2,6,
%T 1,1,0,7,3,2,0,2,0,4,0,8,0,1,3,0,4,5,0,1,0,3,5,9,0,2,0,10,1,0,1,3,0,6,
%U 6,1,0,1,0,11,1,7,2,4,0,2,1,12,0,3,2,13,7,4,0,2,1,8,8,14,3,1,0,0,2,2,0,5,0,5,0
%N Number of prime factors (with multiplicity) of A331598(n), where A331598(n) = A122111(n) / gcd(A122111(n),A241909(n)).
%C Apparently also the number of prime factors (with multiplicity) of A331599(n).
%H Antti Karttunen, <a href="/A331594/b331594.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A001222(A331598(n)).
%t Array[If[# == 1, 0, PrimeOmega[#1/GCD[#1, #2]] & @@ {Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ #], Function[t, Times @@ Prime@ Accumulate[If[Length@ t < 2, {0}, Join[{1}, ConstantArray[0, Length@ t - 2], {-1}]] + ReplacePart[t, Map[#1 -> #2 & @@ # &, #]]]]@ ConstantArray[0, Transpose[#][[1, -1]]] &[# /. {p_, e_} /; p > 0 :> {PrimePi@ p, e}]} &@ FactorInteger[#]] &, 105] (* _Michael De Vlieger_, Jan 25 2020, after _JungHwan Min_ at A122111 *)
%o (PARI) A331594(n) = bigomega(A331598(n));
%Y Cf. A001222, A331598, A331599.
%K nonn
%O 1,10
%A _Antti Karttunen_, Jan 25 2020
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