A331594 Number of prime factors (with multiplicity) of A331598(n), where A331598(n) = A122111(n) / gcd(A122111(n),A241909(n)).

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

Offset: 1

Author

Antti Karttunen, Jan 25 2020

Keywords

• nonn

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
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A001222, A331598, A331599.

Programs

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 *)

PARI

A331594(n) = bigomega(A331598(n));

Formula

a(n) = A001222(A331598(n)).