A323409 Greatest common divisor of Product (p_i^e_i)-1 and n, when n = Product (p_i^e_i); a(n) = gcd(n, A047994(n)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 6, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 4, 1, 2, 5, 14, 3, 2, 1, 12, 1, 2, 3, 1, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 3, 2, 1, 6, 1, 20, 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, Jan 15 2019

Keywords

• nonn

Comments

Records 1, 2, 6, 12, 14, 20, 24, 84, 120, 168, 240, 468, 720, 1008, 1240, 1488, 1632, 7440, 9360, 14880, 32640, ... occur at n = 1, 6, 12, 36, 56, 80, 144, 168, 240, 504, 720, 1404, 3600, 4032, 4960, 8928, 13056, 14880, 28080, 44640, 65280, ...

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A047994, A323410.

Cf. also A009195, A323166, A323406.

Programs

PARI

A047994(n) = { my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1); };
A323409(n) = gcd(n, A047994(n));

Formula

a(n) = gcd(n, A047994(n)), where A047994 is unitary phi.