A329929 a(n) = lcm(tau(n), sigma(n), pod(n)) / gcd(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, 9, 56, 960, 351, 450, 132, 6048, 182, 294, 1800, 158720, 306, 25272, 380, 84000, 14112, 1089, 552, 414720, 11625, 7098, 29160, 32928, 870, 101250, 992, 2064384, 17424, 15606, 58800, 917070336, 1406, 5415, 85176, 11520000, 1722, 777924, 1892

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..43.

Formula

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

a(n) = A336723(n) / A336722(n).

a(p) = p * (p+1) for p = primes.

Example

a(6) = lcm(tau(6), sigma(6), pod(6)) / gcd(tau(6), sigma(6), pod(6)) = lcm(4, 12, 36) / gcd(4, 12, 36) = 36 / 4 = 9.

Mathematica

a[n_] := LCM @@ (t = {(d = DivisorSigma[0, n]), n^(d/2), DivisorSigma[1, n]}) / GCD @@ t; Array[a, 50] (* Amiram Eldar, Aug 31 2020 *)

Prog

(Magma) [LCM([#Divisors(n), &+Divisors(n), &*Divisors(n)]) / GCD([#Divisors(n), &+Divisors(n), &*Divisors(n)]): n in [1..100]]
(PARI) a(n) = my(f=factor(n), v=[numdiv(f), sigma(f), vecprod(divisors(f))]); lcm(v)/gcd(v); \\ Michel Marcus, Aug 31 2020

Crossrefs

Cf. A336722, A336723, A337323.

Cf. A334985 (lcm(n, tau(n), sigma(n), pod(n)) / gcd(n, tau(n), sigma(n), pod(n))).

Sequence in context: A203754 A002922 A334916 * A334985 A336723 A334805

Adjacent sequences: A329926 A329927 A329928 * A329930 A329931 A329932

Keyword

nonn

Author

Jaroslav Krizek, Aug 31 2020

Status

approved