A348929 a(n) = gcd(n, A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e.

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 12, 1, 2, 3, 1, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 1, 36, 1, 2, 1, 2, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 72, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 3, 4, 1, 18, 7, 4, 1, 2, 5, 12, 1, 2, 3, 4, 1, 6, 1, 2, 3

Offset: 1

Author

Antti Karttunen, Nov 07 2021

Keywords

• nonn
• easy
• look

Links

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

Crossrefs

Cf. A003959, A085731, A126865, A323166, A348507, A348928, A348999 [= a(A276086(n))].

Differs from similar A126795 for the first time at n=36, where a(36) = 36, while A126795(36) = 12.

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

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348929(n) = gcd(n, A003959(n));

Formula

a(n) = gcd(n, A003959(n)) = gcd(n, A348507(n)) = gcd(A003959(n), A348507(n)).