A255346 Numbers k such that k and k+1 both have at least two distinct prime factors.

14, 20, 21, 33, 34, 35, 38, 39, 44, 45, 50, 51, 54, 55, 56, 57, 62, 65, 68, 69, 74, 75, 76, 77, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 98, 99, 104, 105, 110, 111, 114, 115, 116, 117, 118, 119, 122, 123, 129, 132, 133, 134, 135, 140, 141, 142, 143, 144, 145, 146, 147, 152, 153, 154

Offset

1,1

Comments

These numbers provide solutions to the problem of finding (x,y) such that x(x+1) | y(y+1) but none of x or x+1 divides any of y or y+1. Namely, these solutions are given for (x,y) being members of the sequence such that x(x+1) divides y(y+1), the smallest of which are (14,20), (14,35), (20,35), ... but, e.g., (14,69) is excluded since 14 | 70.

Contains A074851 as a subsequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

T. Korimort, How many (x,y) satisfy x(x+1)|y(y+1),..., Number Theory group on LinkedIn.com, Feb. 2014.

Mathematica

SequencePosition[Table[If[PrimeNu[n]>1, 1, 0], {n, 200}], {1, 1}][[;; , 1]] (* Harvey P. Dale, Jul 30 2025 *)

Prog

(PARI) for(n=2, 199, omega(n)>=2||(n++&&next); omega(n-1)>=2&&print1((n-1)", "))

Crossrefs

Cf. A074851.

Sequence in context: A006576 A349262 A083247 * A074851 A193672 A087678

Adjacent sequences: A255343 A255344 A255345 * A255347 A255348 A255349

Keyword

nonn,easy

Author

M. F. Hasler, Feb 21 2015

Status

approved