A131960 a(n) = A000043(n) * A000668(n).

6, 21, 155, 889, 106483, 2228207, 9961453, 66571993057, 140656423562035331011, 55088331748199422233011027879, 17361742620725829882898847100829589, 21607930299479592429924287571917281427329

Offset: 1

Author

A.K. Devaraj, Aug 02 2007, Aug 06 2007

Keywords

• nonn
• less

Comments

Note that a(3) = 155 and a(4) = 889 also belong to A119691.

Old name was: Composite numbers such that the first factor is the relevant exponent of Mersenne prime (the second factor).

a(n) is the smallest k > 0 such that A000668(n)^2 divides 2^k-1. Then lpf(2^k-1) = A000668(n), where lpf(m) = A020639(m). - Thomas Ordowski, Feb 03 2019

Links

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

Crossrefs

Cf. A000043, A000668, A002326, A020639, A119691.

Programs

Mathematica

Map[# * (2^#-1) &, MersennePrimeExponent[Range[12]]] (* Amiram Eldar, Oct 21 2024 *)

PARI

expm = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127]; vector(#expm, i, expm[i]*(2^expm[i]-1)) \\ where expm comes from A000043; Michel Marcus, Feb 07 2019

Formula

a(n) = A000043(n)*A000668(n). - R. J. Mathar, Oct 18 2007

a(n) = A002326((A000668(n)^2 - 1)/2). - Thomas Ordowski, Feb 03 2019

Extensions

Terms corrected, edited, and new name by Michel Marcus, Apr 30 2013

a(12) from Michel Marcus, Feb 07 2019