A334663 a(n) = Sum_{d|n} gcd(sigma(d), pod(d)), where pod(k) is the product of the divisors of k (A007955).

1, 2, 2, 3, 2, 15, 2, 4, 3, 5, 2, 20, 2, 7, 6, 5, 2, 19, 2, 8, 4, 7, 2, 33, 3, 5, 4, 64, 2, 93, 2, 6, 6, 5, 4, 25, 2, 7, 4, 19, 2, 69, 2, 12, 10, 7, 2, 38, 3, 7, 12, 8, 2, 44, 4, 73, 4, 5, 2, 124, 2, 7, 6, 7, 4, 167, 2, 8, 6, 27, 2, 41, 2, 5, 8, 12, 4, 43, 2

Offset: 1

Author

Jaroslav Krizek, May 07 2020

Keywords

• nonn

Comments

Inverse Möbius transform of A306682. - Antti Karttunen, May 09 2020

Examples

			a(6) = gcd(sigma(1), pod(1)) + gcd(sigma(2), pod(2)) + gcd(sigma(3), pod(3)) + gcd(sigma(6), pod(6)) = gcd(1, 1) + gcd(3, 2) + gcd(4, 3) + gcd(12, 36) = 1 + 1 + 1 + 12 = 15.
		

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. A334579 (Sum_{d|n} gcd(tau(d), sigma(d))), A334662 (Sum_{d|n} gcd(tau(d), pod(d))).

Cf. A000203 (sigma(n)), A007955 (pod(n)), A306682 (gcd(sigma(n), pod(n))).

Cf. A334731 (product instead of sum).

Programs

Magma

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

PARI

a(n) = sumdiv(n, d, gcd(sigma(d), vecprod(divisors(d)))); \\ Michel Marcus, May 08 2020

Formula

a(p) = 2 for p = primes (A000040).