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).

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

1,2

Links

Table of n, a(n) for n=1..31.

Formula

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

Example

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.

Prog

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

Crossrefs

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))).

Sequence in context: A051784 A158046 A097174 * A325030 A191415 A259130

Adjacent sequences: A334806 A334807 A334808 * A334810 A334811 A334812

Keyword

nonn

Author

Jaroslav Krizek, Aug 01 2020

Status

approved