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A274362
Numbers n such that n and n+1 both have 24 divisors.
3
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.
Sequence in context: A328327 A364861 A237011 * A233871 A182295 A028546
KEYWORD
nonn
AUTHOR
STATUS
approved