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

Author

Charles R Greathouse IV, Jun 19 2016

Keywords

• nonn

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).

Crossrefs

Intersection of A005237 and A137487.

Cf. A000005, A274357, A189982.

Programs

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 *)

PARI

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