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A349774
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Numbers that start a run of four consecutive triangular numbers with four prime factors (counted with multiplicity).
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0
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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