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A255349 Numbers n such that n(n+1) is divisible by some m(m+1) with none of {n, n+1} divisible by any of {m, m+1}. 0


%S 20,35,77,84,98,99,104,119,132,153,174,175,186,189,195,216,224,230,

%T 231,245,246,260,272,279,285,350,351,363,374,384,399,425,429,440,455,

%U 459,494,527,539,551,560,575,594,608,609,615,620,644,645,650,665,696,714,730,735,759,779,780

%N Numbers n such that n(n+1) is divisible by some m(m+1) with none of {n, n+1} divisible by any of {m, m+1}.

%C A subsequence of A255346, see there for further information.

%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.

%e a(1)=20 since 20*21=420 is divisible by 14*15=210 and none of {20, 21} is divisible by any of {14, 15}.

%e a(2)=35 since 35*36 = 1260 is divisible by 14*15 = 210 (and also by 20*21 = 420).

%e 69 is not in the sequence although 69*70 = 4830 is divisible by 14*15 = 210, because 14 divides 70.

%o (PARI) is(n)={omega(n)>=2&&omega(n+1)>=2&&fordiv(n*(n+1),x,x>=n&&return;n*(n+1)%(x*(x+1))&&next;n%x||next;(n+1)%x||next;n%(x+1)||next;(n+1)%(x+1)&&return(1))}

%Y Cf. A074851.

%K nonn

%O 1,1

%A _M. F. Hasler_, Feb 21 2015

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Last modified December 3 11:30 EST 2020. Contains 338900 sequences. (Running on oeis4.)