A323163 Greatest common divisor of product (1+(p^e)) and product p^(e-1), where p ranges over prime factors of n, with e corresponding exponent; a(n) = gcd(A034448(n), A003557(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 3, 10, 1, 1, 1, 2, 1

Offset: 1

Author

Antti Karttunen, Jan 09 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A003557, A034448, A322318, A323159.

Differs from A062760 for the first time at n=36, where a(36) = 2, while A062760(36) = 1.

Programs

PARI

A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A323163(n) = gcd(A003557(n), A034448(n));

Formula

a(n) = gcd(A003557(n), A034448(n)).