A334985 a(n) = lcm(n, tau(n), sigma(n), pod(n)) / gcd(n, tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).

1, 6, 12, 168, 30, 18, 56, 960, 351, 450, 132, 6048, 182, 588, 1800, 158720, 306, 25272, 380, 84000, 14112, 2178, 552, 414720, 11625, 7098, 29160, 32928, 870, 405000, 992, 2064384, 17424, 15606, 58800, 917070336, 1406, 10830, 85176, 11520000, 1722, 3111696

Offset: 1

Author

Jaroslav Krizek, Sep 22 2020

Keywords

• nonn

Examples

			a(6) = lcm(6, tau(6), sigma(6), pod(6)) / gcd(6, tau(6), sigma(6), pod(6))  = lcm(6, 4, 12, 36) / gcd(6, 4, 12, 36) = 36 / 2 = 18.
		

Crossrefs

Cf. A336722, A336723, A337323.

Cf. A329929 (lcm(tau(n), sigma(n), pod(n)) / gcd(tau(n), sigma(n), pod(n))).

Programs

Magma

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

Mathematica

a[n_] := LCM @@ {(d = DivisorSigma[0, n]), (s = DivisorSigma[1, n]), n^(d/2)} / GCD @@ {n, d, s}; Array[a, 50] (* Amiram Eldar, Sep 22 2020 *)

PARI

a(n) = my(f=factor(n), v=[n, numdiv(f), sigma(f), vecprod(divisors(f))]); lcm(v)/gcd(v); \\ Michel Marcus, Sep 22 2020

Formula

a(n) = lcm(tau(n), sigma(n), pod(n)) / gcd(n, tau(n), sigma(n)).

a(n) = A336723(n) / A337323(n).