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%I #21 Dec 16 2018 13:59:55
%S 5984,11780,20349,22815,24794,26144,27675,29799,31724,33579,33824,
%T 34335,34748,36764,37323,37664,38324,38367,38675,38709,40544,41624,
%U 42020,44505,44954,47564,47684,48950,50024,51204,52155,52767,53703,53955,54495,55419
%N Numbers n such that n and n+1 both have 24 divisors.
%C 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.
%H Charles R Greathouse IV, <a href="/A274362/b274362.txt">Table of n, a(n) for n = 1..10000</a>
%H D. A. Goldston, S. W. Graham, J. Pintz, and C. Y. Yıldırım, <a href="http://arxiv.org/abs/0803.2636">Small gaps between almost primes, the parity problem, and some conjectures of Erdos on consecutive integers</a>, arXiv:0803.2636 [math.NT] (2008).
%t 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 *)
%o (PARI) is(n)=numdiv(n)==24 && numdiv(n+1)==24
%Y Intersection of A005237 and A137487.
%Y Cf. A000005, A274357, A189982.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, Jun 19 2016