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 A331594 Number of prime factors (with multiplicity) of A331598(n), where A331598(n) = A122111(n) / gcd(A122111(n),A241909(n)). 3
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS Apparently also the number of prime factors (with multiplicity) of A331599(n). LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A001222(A331598(n)). MATHEMATICA 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 *) PROG (PARI) A331594(n) = bigomega(A331598(n)); CROSSREFS Cf. A001222, A331598, A331599. Sequence in context: A132178 A039655 A103775 * A093057 A065334 A162590 Adjacent sequences:  A331591 A331592 A331593 * A331595 A331596 A331597 KEYWORD nonn AUTHOR Antti Karttunen, Jan 25 2020 STATUS approved

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Last modified April 10 16:05 EDT 2021. Contains 342845 sequences. (Running on oeis4.)