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

2, 3, 4, 7, 8, 16, 31, 127, 256, 8191, 65536, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727

Offset: 1

Author

Zak Seidov, Jan 18 2008

Keywords

• nonn

Comments

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

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

Crossrefs

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

Formula

a(n) = A006549(n+1) for n >= 1 (cf. Robert Israel's comment). - Georg Fischer, Nov 02 2018

Extensions

Missing entry 8 added by N. J. A. Sloane, Jan 22 2018, following a suggestion from Jon E. Schoenfield.