A349774 Numbers that start a run of four consecutive triangular numbers with four prime factors (counted with multiplicity).
161596, 222778, 366796, 962578, 1611910, 2480878, 3301165, 4290985, 13320541, 23588146, 29272726, 43743981, 50818321, 68041945, 79512355, 100614205, 143981965, 161757091, 172896310, 194626585, 200710630, 275338311, 282161890, 352331785, 410712130, 457062495, 457092730
Offset: 1
Keywords
Examples
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).
Programs
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Mathematica
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 *)