A342416 a(n) = gcd(A173557(n), A342001(n)).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 3, 8, 1, 1, 1, 1, 4, 2, 1, 1, 1, 2, 3, 1, 2, 1, 1, 1, 1, 2, 1, 12, 2, 1, 3, 8, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 4, 4, 1, 1, 8, 1, 2, 1, 1, 2, 1, 3, 1, 1, 6, 1, 1, 4, 2, 1, 1, 1, 1, 3, 1, 2, 6, 1, 1, 2, 2, 1, 1, 2, 2, 3, 8, 5, 1, 1, 4, 2, 2, 1, 24, 1, 1, 1, 5, 2, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Mar 11 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A003415, A003557, A173557, A342001, A342413.

Programs

Mathematica

Array[GCD[#2, #1/#3] & @@ {If[#1 < 2, 0, #1 Total[#2/#1 & @@@ #2]], If[#1 == 1, 1, Times @@ Map[# - 1 &, #2[[All, 1]] ]], #1/Times @@ #2[[All, 1]]} & @@ {Abs[#], FactorInteger[#]} &, 91] (* Michael De Vlieger, Mar 11 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342413(n) = gcd(eulerphi(n), A003415(n));
A342416(n) = (A342413(n)/A003557(n));

Formula

a(n) = A342413(n) / A003557(n) = gcd(A173557(n), A342001(n)).