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}.

20, 35, 77, 84, 98, 99, 104, 119, 132, 153, 174, 175, 186, 189, 195, 216, 224, 230, 231, 245, 246, 260, 272, 279, 285, 350, 351, 363, 374, 384, 399, 425, 429, 440, 455, 459, 494, 527, 539, 551, 560, 575, 594, 608, 609, 615, 620, 644, 645, 650, 665, 696, 714, 730, 735, 759, 779, 780

Offset: 1

Author

M. F. Hasler, Feb 21 2015

Keywords

• nonn

Comments

A subsequence of A255346, see there for further information.

Examples

			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}.
a(2)=35 since 35*36 = 1260 is divisible by 14*15 = 210 (and also by 20*21 = 420).
69 is not in the sequence although 69*70 = 4830 is divisible by 14*15 = 210, because 14 divides 70.
		

Links

• 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

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))}