A306682 a(n) = gcd(sigma(n), pod(n)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).

1, 1, 1, 1, 1, 12, 1, 1, 1, 2, 1, 4, 1, 4, 3, 1, 1, 3, 1, 2, 1, 4, 1, 12, 1, 2, 1, 56, 1, 72, 1, 1, 3, 2, 1, 1, 1, 4, 1, 10, 1, 48, 1, 4, 3, 4, 1, 4, 1, 1, 9, 2, 1, 24, 1, 8, 1, 2, 1, 24, 1, 4, 1, 1, 1, 144, 1, 2, 3, 16, 1, 3, 1, 2, 1, 4, 1, 24, 1, 2, 1, 2, 1

Offset: 1

Author

Jaroslav Krizek, Mar 05 2019

Keywords

• nonn

Comments

See A324527(n) = the smallest numbers k such that a(k) = n.

Examples

			For n=6: a(6) = gcd(tau(6), pod(6)) = gcd(4, 36) = 4.
		

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. A000005, A000203, A007955, A009205, A046642, A120736, A324526, A324527.

Programs

Magma

[GCD(SumOfDivisors(n), &*[d: d in Divisors(n)]): n in [1.. 100]]

PARI

a(n) = my(d=divisors(n)); gcd(vecsum(d), vecprod(d)); \\ Michel Marcus, Mar 05 2019

Formula

a(n) = 1 for numbers in A014567.

a(n) = tau(n) for numbers in A324526.