%I #21 Dec 04 2021 05:52:21

%S 161596,222778,366796,962578,1611910,2480878,3301165,4290985,13320541,

%T 23588146,29272726,43743981,50818321,68041945,79512355,100614205,

%U 143981965,161757091,172896310,194626585,200710630,275338311,282161890,352331785,410712130,457062495,457092730

%N Numbers that start a run of four consecutive triangular numbers with four prime factors (counted with multiplicity).

%e a(1) = 161596 because 161596 is the smallest number in the first set of four consecutive triangular numbers with four prime factors (counted with multiplicity), i.e., (161596 = 2*2*71*569, 162165 = 3*5*19*569, 162735 = 3*5*19*571, 163306 = 2*11*13*571).

%t t[n_] := n*(n + 1)/2; q[n_] := PrimeOmega[n] == 4; Select[Partition[t /@ Range[35000], 4, 1], AllTrue[#, q] &][[;; , 1]] (* _Amiram Eldar_, Nov 29 2021 *)

%Y Cf. A000217, A128905, A349773.

%K nonn

%O 1,1

%A _Shyam Sunder Gupta_, Nov 29 2021