A123476 a(n) = (n!)^2/phi(n!), where phi is Euler's totient function.

1, 4, 18, 72, 450, 2700, 22050, 176400, 1587600, 15876000, 192099600, 2305195200, 32464832400, 454507653600, 6817614804000, 109081836864000, 1970290678356000, 35465232210408000, 711274934886516000, 14225498697730320000, 298735472652336720000, 6572180398351407840000

Offset

1,2

Comments

a(n) is a solution to the equation phi(x) = n!.

1/a(n) is the asymptotic density of the numbers that are unitarily divisible by n! (see formula and A391901). - Amiram Eldar, Dec 23 2025

Links

T. D. Noe, Table of n, a(n) for n=1..100

P. Erdös and J. Lambek, Problem 4221, Amer. Math. Monthly, 55 (1948), 103.

Formula

a(n) = A373319(n!)/A373318(n!). - Amiram Eldar, Dec 23 2025

Mathematica

Table[(n!)^2/EulerPhi[n!], {n, 20}] (* Harvey P. Dale, Nov 29 2015 *)

Prog

(PARI) a(n) = (n!)^2/eulerphi(n!); \\ Michel Marcus, Jul 11 2018

Crossrefs

Cf. A000010, A000142, A002202 (values taken by phi(x)), A373318, A373319, A391901.

Cf. A055487 (least m such that phi(m) = n!).

Sequence in context: A267450 A199524 A083693 * A343580 A027905 A037497

Adjacent sequences: A123473 A123474 A123475 * A123477 A123478 A123479

Keyword

nonn

Author

T. D. Noe, Sep 27 2006

Status

approved