A349773 Numbers that start a run of four consecutive triangular numbers with four distinct prime factors.
16653, 16836, 17020, 17205, 17391, 27495, 29890, 30135, 50721, 51040, 51360, 51681, 70125, 81003, 81406, 84255, 84666, 85078, 85491, 85905, 89676, 90100, 110215, 110685, 111156, 142311, 181503, 214185, 222111, 222778, 305371, 306153, 344865, 345696, 355746, 356590
Offset: 1
Keywords
Examples
a(1) = 16653 because 16653 is the smallest number in the first set of four consecutive triangular numbers with four distinct prime factors, i.e., 16653 = 3*7*13*61, 16836 = 2^2*3*23*61, 17020 = 2^2*5*23*37, 17205 = 3*5*31*37.
Programs
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Mathematica
t[n_] := n*(n + 1)/2; q[n_] := PrimeNu[n] == 4; Select[Partition[t /@ Range[1000], 4, 1], AllTrue[#, q] &][[;; , 1]] (* Amiram Eldar, Nov 29 2021 *)