

A255346


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


5



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
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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

Table of n, a(n) for n=1..64.
T. Korimort, How many (x,y) satisfy x(x+1)y(y+1),..., Number Theory group on LinkedIn.com, Feb. 2014.


PROG

(PARI) for(n=2, 199, omega(n)>=2(n++&&next); omega(n1)>=2&&print1((n1)", "))


CROSSREFS

Cf. A074851.
Sequence in context: A144080 A006576 A083247 * A074851 A193672 A087678
Adjacent sequences: A255343 A255344 A255345 * A255347 A255348 A255349


KEYWORD

nonn,easy


AUTHOR

M. F. Hasler, Feb 21 2015


STATUS

approved



