cp's OEIS Frontend

A144524 Triangular numbers n*(n+1)/2 with n composite, where number of prime factors of n, counted with multiplicity, is less than the number of prime factors in n+1.

%I A144524 #12 Aug 10 2025 06:03:23
%S A144524 120,351,630,780,1225,1326,1540,1953,2016,2145,2415,2775,3003,3828,
%T A144524 4186,4560,4950,6216,6670,7140,7626,7875,8385,9045,10296,10731,12090,
%U A144524 12720,13041,14365,15400,16836,17205,17578,17766,18915,19110,20706,21321,21528
%N A144524 Triangular numbers n*(n+1)/2 with n composite, where number of prime factors of n, counted with multiplicity, is less than the number of prime factors in n+1.
%e A144524 If n = 15 = 2*3 (number of prime factors = 2) and n+1 = 16 = 2*2*2*2 (number of prime factors = 4), then 15*16/2 = 120 = a(1). If n = 26 = 2*13 (number of prime factors = 2) and n+1 = 27 = 3*3*3 (number of prime factors = 3), then 26*27/2 = 351 = a(2). If n = 35 = 5*7 (number of prime factors = 2) and n+1 = 36 = 2*2*3*3 (number of prime factors = 4), then 35*36/2 = 630 = a(3), etc.
%t A144524 fQ[n_] := !PrimeQ@ n && Plus @@ Last /@ FactorInteger@n < Plus @@ Last /@ FactorInteger[n + 1]; # (# + 1)/2 & /@ Select[ Range@ 209, fQ@# &] (* _Robert G. Wilson v_, Dec 21 2008 *)
%Y A144524 Cf. A000040, A000392.
%K A144524 nonn
%O A144524 1,1
%A A144524 _Juri-Stepan Gerasimov_, Dec 15 2008
%E A144524 Edited by _Robert G. Wilson v_, Dec 21 2008