A349773
Numbers that start a run of four consecutive triangular numbers with four distinct prime factors.
Original entry on oeis.org
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
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.
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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 *)
A349774
Numbers that start a run of four consecutive triangular numbers with four prime factors (counted with multiplicity).
Original entry on oeis.org
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
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).
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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 *)
Showing 1-2 of 2 results.