A072696 a(n) = lcm(d(n^3), d(n)), where d(n) = A000005, the number of divisors of n.

1, 4, 4, 21, 4, 16, 4, 20, 21, 16, 4, 84, 4, 16, 16, 65, 4, 84, 4, 84, 16, 16, 4, 40, 21, 16, 20, 84, 4, 64, 4, 48, 16, 16, 16, 441, 4, 16, 16, 40, 4, 64, 4, 84, 84, 16, 4, 260, 21, 84, 16, 84, 4, 40, 16, 40, 16, 16, 4, 336, 4, 16, 84, 133, 16, 64, 4, 84, 16, 64, 4, 420, 4, 16

Offset

1,2

Comments

If n is a product of k distinct primes, then a(n) = 4^k.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from exponents in factorization of n.

Index entries for sequences related to LCM.

Mathematica

Table[LCM[DivisorSigma[0, n^3], DivisorSigma[0, n]], {n, 80}] (* Wesley Ivan Hurt, Nov 25 2017 *)

Prog

(PARI) A072696(n) = lcm(numdiv(n), numdiv(n^3)); \\ Antti Karttunen, Nov 24 2017
(PARI) a(n) = {my(e = factor(n)[, 2]); lcm(vecprod(apply(x -> 3*x+1, e)), vecprod(apply(x -> x+1, e))); } \\ Amiram Eldar, Dec 02 2023

Crossrefs

Cf. A000005, A072695.

Sequence in context: A270376 A323744 A205142 * A075219 A264650 A272450

Adjacent sequences: A072693 A072694 A072695 * A072697 A072698 A072699

Keyword

easy,nonn

Author

Labos Elemer, Jul 04 2002

Status

approved