A274362 -id:A274362 - cp's OEIS frontend

A274357 Numbers n such that n and n+1 both have 8 divisors.

104, 135, 189, 230, 231, 285, 296, 344, 374, 375, 429, 434, 609, 645, 663, 664, 741, 776, 782, 805, 874, 902, 903, 969, 986, 1001, 1015, 1022, 1029, 1065, 1085, 1095, 1105, 1106, 1112, 1130, 1161, 1208, 1221, 1245, 1265, 1269, 1309, 1310, 1334, 1335, 1374, 1406, 1431

Offset: 1

Charles R Greathouse IV, Jun 19 2016

nonn

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

Intersection of A005237 and A030626.
Numbers n such that n and n+1 both have k divisors: A039832 (k=4), A049103 (k=6), A274357 (k=8), A215197 (k=10), A174456 (k=12), A274358 (k=14), A274359 (k=16), A274360 (k=18), A274361 (k=20), A274366 (k=22), A274362 (k=24), A274363 (k=26), A274364 (k=28), A274365 (k=30).
Cf. A000005.

SequencePosition[DivisorSigma[0,Range[2000]],{8,8}][[All,1]] (* Harvey P. Dale, Sep 07 2021 *)

PARI
```
is(n)=numdiv(n)==8 && numdiv(n+1)==8
```

A336658 Numbers k such that k and k+1 both have the prime signature (2,1,1,1) (A189982).

Original entry on oeis.org

11780, 20349, 24794, 33579, 36764, 37323, 38324, 38675, 38709, 42020, 44505, 47564, 47684, 51204, 52155, 53955, 55419, 56259, 64844, 68475, 71379, 71994, 75284, 77714, 79134, 80475, 81548, 81549, 83420, 85491, 86715, 87164, 87380, 90524, 92364, 94940, 95403, 95589

Offset: 1

Amiram Eldar, Jul 28 2020

nonn

Goldston et al. (2011) proved that this sequence is infinite.

Some consecutive terms are (81548, 81549), (141218, 141219), (179828, 179829). - David A. Corneth, Jul 29 2020

			11780 is a term since 11780 = 2^2 * 5 * 19 * 31 and 11781 = 3^2 * 7 * 11 * 17.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Daniel A. Goldston, Sidney W. Graham, Janos Pintz, and Cem Y. Yıldırım, Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers, International Mathematics Research Notices, Vol. 2011, No. 7 (2011), pp. 1439-1450, preprint, arXiv:0803.2636 [math.NT], 2006.

Subsequence of A140078 and A274362.

Cf. A189982.

seqQ[n_] := Sort[FactorInteger[n][[;; , 2]]] == {1, 1, 1, 2}; Select[Range[10^5], seqQ[#] && seqQ[# + 1] &]

cp's OEIS Frontend

A274357 Numbers n such that n and n+1 both have 8 divisors.

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