A331597 a(n) = A007947(A331595(n)).

1, 2, 2, 3, 2, 3, 2, 5, 3, 3, 2, 5, 2, 3, 6, 7, 2, 15, 2, 5, 6, 3, 2, 7, 3, 3, 5, 5, 2, 15, 2, 11, 6, 3, 6, 7, 2, 3, 6, 7, 2, 15, 2, 5, 10, 3, 2, 11, 3, 15, 6, 5, 2, 7, 6, 7, 6, 3, 2, 7, 2, 3, 10, 13, 6, 15, 2, 5, 6, 15, 2, 11, 2, 3, 15, 5, 6, 15, 2, 11, 7, 3, 2, 7, 6, 3, 6, 7, 2, 7, 6, 5, 6, 3, 6, 13, 2, 15, 10, 7, 2, 15, 2, 7, 30

Offset: 1

Author

Antti Karttunen, Jan 22 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A007947, A064989, A122111, A241909, A331595, A331596.

Programs

Mathematica

Array[Times @@ FactorInteger[#][[All, 1]] &@ If[# == 1, 1, GCD @@ {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 24 2020, after JungHwan Min at A122111 *)

PARI

A331597(n) = factorback(factorint(gcd(A122111(n), A241909(n)))[, 1]);

Formula

a(n) = A007947(A331595(n)) = A007947(gcd(A122111(n), A241909(n))).