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

Author

M. F. Hasler, Feb 21 2015

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A074851.

Programs

Mathematica

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

PARI

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