login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A134459 Numbers n such that lcm(1,...,n-1) < lcm(1,...,n) < lcm(1,...,n+1). 2
2, 3, 4, 7, 8, 16, 31, 127, 256, 8191, 65536, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..18.

FORMULA

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

CROSSREFS

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

Sequence in context: A281782 A334020 A006549 * A225211 A159554 A256606

Adjacent sequences:  A134456 A134457 A134458 * A134460 A134461 A134462

KEYWORD

nonn

AUTHOR

Zak Seidov, Jan 18 2008

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 13:27 EST 2022. Contains 358362 sequences. (Running on oeis4.)