A348928 a(n) = gcd(n, A003958(n)), where A003958 is multiplicative with a(p^e) = (p-1)^e.

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

Offset: 1

Author

Antti Karttunen, Nov 07 2021

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A003958, A085731, A126865, A322582, A348929, A348998 [= a(A276086(n))].

Differs from similar A126864 for the first time at n=36, where a(36) = 4, while A126864(36) = 2.

Programs

Mathematica

f[p_, e_] := (p - 1)^e; a[n_] := GCD[n, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Nov 07 2021 *)

PARI

A003958(n) = if(1==n,n,my(f=factor(n)); for(i=1,#f~,f[i,1]--); factorback(f));
A348928(n) = gcd(n, A003958(n));

Formula

a(n) = gcd(n, A003958(n)) = gcd(n, A322582(n)) = gcd(A003958(n), A322582(n)).