A051418 Square of LCM of {1, 2, ..., n}.

1, 4, 36, 144, 3600, 3600, 176400, 705600, 6350400, 6350400, 768398400, 768398400, 129859329600, 129859329600, 129859329600, 519437318400, 150117385017600, 150117385017600, 54192375991353600, 54192375991353600, 54192375991353600, 54192375991353600

Offset: 1

Author

Asher Auel

Keywords

• easy
• nice
• nonn

Comments

a(n) is the least common multiple (or LCM) of {1, 4, 9, 16, ..., n^2}.

Examples

			a(5) = lcm {1, 4, 9, 16, 25} = 3600.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..200
• Jon T. Butler, Tsutomu Sasao, Realizing all Index Generation Functions by the Row-Shift Method, IEEE 49th International Symposium on Multiple-Valued Logic (ISMVL 2019).
• Index entries for sequences related to lcm's

Crossrefs

Cf. A003418.

Programs

Mathematica

Table[LCM@@Range[n],{n,20}]^2  (* Harvey P. Dale, Mar 28 2011 *)

Python

# generator of sequence
from math import lcm
from itertools import accumulate, count, islice
def sqr(x): return x*x
def agen(): yield from map(sqr, accumulate(count(1), lcm))
print(list(islice(agen(), 22))) # Michael S. Branicky, Oct 04 2022

Formula

a(n) = A003418(n)^2.