A344877 a(n) = gcd(n, A344875(n)), where A344875 is multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e -1 for odd primes p.

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 6, 1, 4, 3, 2, 1, 6, 1, 2, 1, 14, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 20, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 6, 5, 2, 3, 2, 1, 4, 1, 2, 3, 1, 1, 6, 1, 4, 1, 2, 1, 24, 1, 2, 3, 2, 1, 6, 1, 4, 1, 2, 1, 84, 1, 2, 1, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 1, 4, 1, 6, 1, 4, 3

Offset: 1

Author

Antti Karttunen, Jun 03 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A344875.

Cf. also A323409.

Programs

Mathematica

f[2, e_] := 2^(e + 1) - 1; f[p_, e_] := p^e - 1; a[1] = 1; a[n_] := GCD[n, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Jun 03 2021 *)

PARI

A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
A344877(n) = gcd(n, A344875(n));