cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A298410 #36 Aug 18 2019 16:34:16
%S A298410 2,6,12,420,840,720720,72201776446800,
%T A298410 6676878045498705789701874602220118271269436344024536000,
%U A298410 16674490806895842671659008751776385350270324508909651849955453691538889375930032935391666564679008085339616000
%N A298410 Unique least common multiples for {1,2,...,n}.
%C A298410 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).
%C A298410 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.
%F A298410 a(n) = A003418(A134459(n)). - _Michel Marcus_, Jan 23 2018
%e A298410 lcm(1,2,...,7) is 420 and lcm(1,2,...,7,2^3) is 840 so 420 and 840 are in the sequence.
%e A298410 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.
%Y A298410 Cf. A003418, A051451, A134459.
%K A298410 nonn
%O A298410 1,1
%A A298410 _Adrian Pietkiewicz_, Jan 18 2018