A298410 Unique least common multiples for {1,2,...,n}.

2, 6, 12, 420, 840, 720720, 72201776446800, 6676878045498705789701874602220118271269436344024536000, 16674490806895842671659008751776385350270324508909651849955453691538889375930032935391666564679008085339616000

Offset

1,1

Comments

This is a subset of A003418 such that lcm(1,2,...,n-1) <> lcm(1,2,...,n) <> lcm(1,2,...,n+1) for (n>=1).

lcm(1,2,...,n) will be unique if both n and n+1 can be expressed as different prime powers, i.e., n = p^a and n+1 = q^b where p,q are prime and a,b are integers.

Links

Table of n, a(n) for n=1..9.

Formula

a(n) = A003418(A134459(n)). - Michel Marcus, Jan 23 2018

Example

lcm(1,2,...,7) is 420 and lcm(1,2,...,7,2^3) is 840 so 420 and 840 are in the sequence.
But lcm(1,2,...,7,2^3,3^2) = lcm(1,2...,7,2^3,3^2,(2*5)) = 2520. If n=9, n+1 is not a prime power and 2520 is not unique. So 2520 is not in the sequence.

Crossrefs

Cf. A003418, A051451, A134459.

Sequence in context: A309743 A291062 A058046 * A367314 A328448 A074180

Adjacent sequences: A298407 A298408 A298409 * A298411 A298412 A298413

Keyword

nonn

Author

Adrian Pietkiewicz, Jan 18 2018

Status

approved