A338563 a(n) = lcm(n, tau(n), sigma(n)) where tau(k) is the number of divisors of k (A000005) and sigma(k) is the sum of divisors of k (A000203).

1, 6, 12, 84, 30, 12, 56, 120, 117, 180, 132, 84, 182, 168, 120, 2480, 306, 234, 380, 420, 672, 396, 552, 120, 2325, 1092, 1080, 168, 870, 360, 992, 2016, 528, 1836, 1680, 3276, 1406, 1140, 2184, 360, 1722, 672, 1892, 924, 1170, 1656, 2256, 7440, 2793, 4650

Offset: 1

Author

Jaroslav Krizek, Nov 02 2020

Keywords

• nonn

Examples

			a(6) = lcm(6, tau(6), sigma(6)) = lcm(6, 4, 12) = 12.
		

Crossrefs

Cf. A000005, A000203.

Cf. A337323 (gcd(n, tau(n), sigma(n))), A324528 (lcm(n, tau(n), pod(n))), A324529 (lcm(n, sigma(n), pod(n))).

Programs

Magma

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

Mathematica

a[n_] := LCM @@ {n, DivisorSigma[0, n], DivisorSigma[1, n]}; Array[a, 50] (* Amiram Eldar, Nov 03 2020 *)

PARI

a(n) = my(f=factor(n)); lcm([n, sigma(f), numdiv(f)]); \\ Michel Marcus, Nov 03 2020

Formula

a(p) = p *(p + 1) for p = primes (A000040).