A334731 -id:A334731 - cp's OEIS frontend

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

Jaroslav Krizek, May 07 2020

nonn

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

			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.

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

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).

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

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

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

A334809 a(n) = Product_{d|n} lcm(sigma(d), pod(d)) where sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).

Original entry on oeis.org

1, 6, 12, 336, 30, 2592, 56, 322560, 4212, 162000, 132, 1755758592, 182, 395136, 648000, 10239344640, 306, 68976790272, 380, 1524096000000, 9483264, 3449952, 552, 2796089100573081600, 116250, 15502032, 122821920, 485745426432, 870, 102036672000000000, 992

Offset: 1

Jaroslav Krizek, Aug 01 2020

nonn

			a(6) = lcm(sigma(1), pod(1)) * lcm(sigma(2), pod(2)) * lcm(sigma(3), pod(3)) * lcm(sigma(6), pod(6)) = lcm(1, 1) * lcm(3, 2) * lcm(4, 3) * lcm(12, 36) = 1 * 6 * 12 * 36 = 2592.

Cf. A334794 (Sum_{d|n} lcm(sigma(d), pod(d))), A334731 (Product_{d|n} gcd(sigma(d), pod(d))).

Cf. A000203(sigma(n)), A007955 (pod(n)), A324529 (lcm(sigma(n), pod(n))).

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

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

cp's OEIS Frontend

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

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