A334662 a(n) = Sum_{d|n} gcd(tau(d), pod(d)), where pod(k) is the product of the divisors of k (A007955).

1, 3, 2, 4, 2, 8, 2, 8, 5, 8, 2, 15, 2, 8, 4, 9, 2, 17, 2, 11, 4, 8, 2, 27, 3, 8, 6, 11, 2, 22, 2, 11, 4, 8, 4, 33, 2, 8, 4, 23, 2, 22, 2, 11, 10, 8, 2, 30, 3, 11, 4, 11, 2, 26, 4, 23, 4, 8, 2, 43, 2, 8, 10, 12, 4, 22, 2, 11, 4, 22, 2, 57, 2, 8, 8, 11, 4, 22

Offset: 1

Author

Jaroslav Krizek, May 07 2020

Keywords

• nonn

Comments

Inverse Möbius transform of A306671. - Antti Karttunen, May 19 2020

Examples

			a(6) = gcd(tau(1), pod(1)) + gcd(tau(2), pod(2)) + gcd(tau(3), pod(3)) + gcd(tau(6), pod(6)) = gcd(1, 1) + gcd(2, 2) + gcd(2, 3) + gcd(4, 36) = 1 + 2 + 1 + 4 = 8.
		

Links

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

Crossrefs

Cf. A334579 (Sum_{d|n} gcd(tau(d), sigma(d))), A334663 (Sum_{d|n} gcd(sigma(d), pod(d))).

Cf. A000005 (tau(n)), A007955 (pod(n)), A306671 (gcd(tau(n), pod(n))).

Programs

Magma

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

PARI

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

Formula

a(p) = 2 for p = odd primes (A065091).