A334806 a(n) = Product_{d|n} lcm(tau(d), sigma(d)) where tau(k) is the number of divisors of k (A000005) and sigma(k) is the sum of divisors of k (A000203).

1, 6, 4, 126, 6, 288, 8, 7560, 156, 1296, 12, 508032, 14, 1152, 576, 1171800, 18, 876096, 20, 1143072, 1024, 2592, 24, 3657830400, 558, 7056, 6240, 4064256, 30, 107495424, 32, 147646800, 2304, 11664, 2304, 1265709908736, 38, 7200, 3136, 24690355200, 42

Offset: 1

Author

Jaroslav Krizek, Jun 26 2020

Keywords

• nonn

Examples

			a(6) = lcm(tau(1), sigma(1)) * lcm(tau(2), sigma(2)) * lcm(tau(3), sigma(3)) * lcm(tau(6), sigma(6)) = lcm(1, 1) * lcm(2, 3) * lcm(2, 4) * lcm(4, 12) = 1 * 6 * 4 * 12 = 288.
		

Crossrefs

Cf. A334784 (Sum_{d|n} lcm(tau(d), sigma(d))), A334729 (Product_{d|n} gcd(tau(d), sigma(d))).

Cf. A000005 (tau(n)), A000203 (sigma(n)), A009278 (lcm(tau(n), sigma(n))).

Programs

Magma

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

Mathematica

a[n_] := Product[LCM[DivisorSigma[0, d], DivisorSigma[1, d]], {d, Divisors[n]}]; Array[a, 41] (* Amiram Eldar, Jun 27 2020 *)

PARI

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

Formula

a(p) = p + 1 for p = odd primes (A065091).