A323166 Greatest common divisor of Product (1+(p_i^e_i)) and n, when n = Product (p_i^e_i); a(n) = gcd(A034448(n), n).

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 6, 1, 10, 1, 2, 1, 12, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 4, 15, 2, 1, 4, 1, 2, 3, 2, 1, 6, 1, 8, 1, 2, 1, 60, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 18, 1, 2, 1, 4, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 3, 4, 1, 90, 7, 4, 1, 2, 5, 12, 1, 2, 3, 10, 1, 6, 1, 2, 3

Offset: 1

Author

Antti Karttunen, Jan 09 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A034448, A323160, A323163.

Programs

PARI

A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A323166(n) = gcd(n, A034448(n));

Formula

a(n) = gcd(n, A034448(n)), where A034448 is usigma, the sum of unitary divisors of n.