A334805 a(n) = Product_{d|n} lcm(d, sigma(d)) where sigma(k) is the sum of divisors of k (A000203).

1, 6, 12, 168, 30, 864, 56, 20160, 1404, 16200, 132, 2032128, 182, 56448, 43200, 9999360, 306, 23654592, 380, 190512000, 451584, 313632, 552, 29262643200, 23250, 596232, 1516320, 88510464, 870, 100776960000, 992, 20158709760, 836352, 1685448, 2822400

Offset: 1

Author

Jaroslav Krizek, Jun 26 2020

Keywords

• nonn

Examples

			a(6) = lcm(1, sigma(1)) * lcm(2, sigma(2)) * lcm(3, sigma(3)) * lcm(6, sigma(6)) = lcm(1, 1) * lcm(2, 3) * lcm(3, 4) * lcm(6, 12) = 1 * 6 * 12 * 12 = 864.
		

Crossrefs

Cf. A334783 (Sum_{d|n} lcm(d, sigma(d))), A334491 (Product_{d|n} gcd(d, sigma(d))).

Cf. A000203 (sigma(n)), A009242 (lcm(n, sigma(n))), A036690.

Programs

Magma

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

Mathematica

a[n_] := Product[LCM[d, DivisorSigma[1, d]], {d, Divisors[n]}]; Array[a, 35] (* Amiram Eldar, Jun 27 2020 *)

PARI

a(n) = my(d=divisors(n)); prod(k=1, #d, lcm(d[k], sigma(d[k]))); \\ Michel Marcus, Jun 27 2020

Formula

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