A274362 Numbers n such that n and n+1 both have 24 divisors.

5984, 11780, 20349, 22815, 24794, 26144, 27675, 29799, 31724, 33579, 33824, 34335, 34748, 36764, 37323, 37664, 38324, 38367, 38675, 38709, 40544, 41624, 42020, 44505, 44954, 47564, 47684, 48950, 50024, 51204, 52155, 52767, 53703, 53955, 54495, 55419

Offset

1,1

Comments

Goldston-Graham-Pintz-Yildirim prove that this sequence is infinite; in particular infinitely often a(k) = A189982(n) = A189982(n+1) - 1. In fact, their proof shows that at least one of the residue classes 355740n + 47480, 889350n + 118700, or 592900n + 79134 contains infinitely many terms of this sequence.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

D. A. Goldston, S. W. Graham, J. Pintz, and C. Y. Yıldırım, Small gaps between almost primes, the parity problem, and some conjectures of Erdos on consecutive integers, arXiv:0803.2636 [math.NT] (2008).

Mathematica

Reap[For[k = 1, k < 56000, k++, If[DivisorSigma[0, k] == DivisorSigma[0, k + 1] == 24, Sow[k]]]][[2, 1]] (* Jean-François Alcover, Dec 16 2018 *)

Prog

(PARI) is(n)=numdiv(n)==24 && numdiv(n+1)==24

Crossrefs

Intersection of A005237 and A137487.

Cf. A000005, A274357, A189982.

Sequence in context: A328327 A364861 A237011 * A233871 A182295 A028546

Adjacent sequences: A274359 A274360 A274361 * A274363 A274364 A274365

Keyword

nonn

Author

Charles R Greathouse IV, Jun 19 2016

Status

approved