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A134459 Numbers n such that lcm(1,...,n-1) < lcm(1,...,n) < lcm(1,...,n+1). 2


%S 2,3,4,7,8,16,31,127,256,8191,65536,131071,524287,2147483647,

%T 2305843009213693951,618970019642690137449562111,

%U 162259276829213363391578010288127,170141183460469231731687303715884105727

%N Numbers n such that lcm(1,...,n-1) < lcm(1,...,n) < lcm(1,...,n+1).

%C Or, numbers n such that A003418(n-1) < A003418(n) < A003418(n+1). Sequence is the union(A019434 - 1, A000668).

%C lcm(1..n-1) < lcm(1..n) iff n is a prime power. So the sequence consists of those n for which both n and n+1 are prime powers. By Catalan's conjecture (proved by Mihailescu), the only case where n and n+1 are both powers > 1 is n=8. Otherwise, whichever of n and n+1 is even must be a power of 2 and the other must be a prime: either a Mersenne prime if n+1 is the power of 2, or a Fermat prime if n is the power of 2. - _Robert Israel_

%F a(n) = A006549(n+1) for n >= 1 (cf. Robert Israel's comment). - _Georg Fischer_, Nov 02 2018

%Y Cf. A000668, A003418, A006549, A019434. Essentially a duplicate of A068194.

%K nonn

%O 1,1

%A _Zak Seidov_, Jan 18 2008

%E Missing entry 8 added by _N. J. A. Sloane_, Jan 22 2018, following a suggestion from _Jon E. Schoenfield_.

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Last modified April 3 15:51 EDT 2020. Contains 333197 sequences. (Running on oeis4.)