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A349773
Numbers that start a run of four consecutive triangular numbers with four distinct prime factors.
1
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
1,1
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Shyam Sunder Gupta, Nov 29 2021
STATUS
approved