A055774 - OEIS

A055774

Least common multiple of n! and n^n.

1, 4, 54, 768, 75000, 233280, 592950960, 5284823040, 1735643790720, 5670000000000, 1035338990313196800, 17163493362892800, 145077660657859734604800, 9653278129532887449600, 6283924459312500000000000, 11778483592893497717293056000, 17308174186341918654885176242176000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

a(n) = lcm(A000312(n), A000142(n)) = A000312(n)*A000142(n)/A051696(n).

MAPLE

A055774:=n->lcm(n!, n^n): seq(A055774(n), n=1..15); # Wesley Ivan Hurt, Jul 07 2014

MATHEMATICA

Table[LCM[n!, n^n], {n, 15}] (* Wesley Ivan Hurt, Jul 07 2014 *)

PROG

(GAP) List([1..200], n->Lcm(Factorial(n), n^n)); # Muniru A Asiru, Feb 04 2018

(PARI) a(n) = lcm(n!, n^n); \\ Michel Marcus, Feb 06 2018

(Python)

from math import factorial

from sympy import factorint

from sympy.ntheory.factor_ import digits

def A055774(n):

c = factorial(n)*n**n

for p, e in factorint(n).items():

c //= p**min(e*n, (n-sum(digits(n, p)[1:]))//(p-1))

return c # Chai Wah Wu, May 03 2026

CROSSREFS

Cf. A000142 (n!), A000312 (n^n), A051696 (gcd).

Sequence in context: A241126 A089205 A294041 * A071248 A221611 A303048

Adjacent sequences: A055771 A055772 A055773 * A055775 A055776 A055777

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Jul 12 2000

EXTENSIONS

More terms from James Sellers, Jul 13 2000

STATUS

approved