A144523 Triangular numbers n*(n+1)/2 with n and n+1 composite, where number of prime factors in n > number of prime factors in n+1.

36, 210, 300, 528, 1035, 1176, 1275, 1485, 1596, 2080, 2346, 2926, 3240, 3321, 3570, 4095, 4278, 5460, 5565, 6105, 6555, 6903, 7260, 8256, 8778, 9870, 10440, 11628, 11935, 12880, 13695, 14196, 15576, 16653, 17020, 17391, 17955, 20100, 20910, 21736, 22578, 23436, 24310, 25200, 25425

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 15 2008

Keywords

• nonn

Comments

Subsequence of A144291 - R. J. Mathar, Jan 17 2009

Prime factors counted with multiplicity. - Harvey P. Dale, Aug 23 2020

Examples

			If n=8=2*2*2(number of prime factors = 3) and n+1=9=3*3(number of prime factors = 2), then 8*9/2=36=a(1). If n=20=2*2*5(number of prime factors = 3) and n+1=21=3*7(number of prime factors = 2), then 20*21/2=210=a(2). If n=24=2*2*2*3(number of prime factors = 4) and n+1=25=5*5(number of prime factors = 2), then 24*25/2=300=a(3), etc.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000392, A141468, A152622.

Programs

Mathematica

(Times@@#)/2&/@Select[Partition[Range[250],2,1],AllTrue[ #,CompositeQ] && PrimeOmega[#[[1]]]>PrimeOmega[#[[2]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 23 2020 *)

Extensions

Corrected definition. 2926 inserted and extended. - R. J. Mathar, Jan 17 2009