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%I #6 Feb 21 2015 12:21:36
%S 14,20,21,33,34,35,38,39,44,45,50,51,54,55,56,57,62,65,68,69,74,75,76,
%T 77,84,85,86,87,90,91,92,93,94,95,98,99,104,105,110,111,114,115,116,
%U 117,118,119,122,123,129,132,133,134,135,140,141,142,143,144,145,146,147,152,153,154
%N Numbers n such that n and n+1 both have at least two distinct prime factors.
%C 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.
%C Contains A074851 as a subsequence.
%H T. Korimort, <a href="https://www.linkedin.com/groups/Let-x-y-be-positive-4510047.S.5973962079390941188">How many (x,y) satisfy x(x+1)|y(y+1),...</a>, Number Theory group on LinkedIn.com, Feb. 2014.
%o (PARI) for(n=2,199,omega(n)>=2||(n++&&next);omega(n-1)>=2&&print1((n-1)","))
%Y Cf. A074851.
%K nonn,easy
%O 1,1
%A _M. F. Hasler_, Feb 21 2015
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