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 A334129 Numbers that can be written as a product of one or more consecutive triangular numbers. 2
 0, 1, 3, 6, 10, 15, 18, 21, 28, 36, 45, 55, 60, 66, 78, 91, 105, 120, 136, 150, 153, 171, 180, 190, 210, 231, 253, 276, 300, 315, 325, 351, 378, 406, 435, 465, 496, 528, 561, 588, 595, 630, 666, 703, 741, 780, 820, 861, 900, 903, 946, 990, 1008, 1035 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Triangular Number MATHEMATICA lmt = 1050; t = PolygonalNumber[3, #] & /@ Range[0, Sqrt[ 2lmt]]; f[n_] := Select[ Times @@@ Partition[t, n +1, 1], # < lmt &]; lst = {}; k = 0; While[f@k != {}, lst = Join[lst, f@k]; k++]; Union@lst (* Robert G. Wilson v, Apr 16 2020 *) PROG (PARI) list(lim)=if(lim<1, return(if(lim<0, [], [0]))); my(v=List([0, 1]), t=1, m=2); lim\=1; while(t<=lim, listput(v, t); t=m*m++/2); for(e=1, m, for(i=3, m-e, t=factorback(Vec(v[i..i+e])); if(t>lim, break); listput(v, t))); Set(v) \\ Charles R Greathouse IV, Apr 16 2020 CROSSREFS Cf. A000217, A006472, A085780, A085782, A334130. Sequence in context: A083266 A334130 A054731 * A282064 A029716 A284521 Adjacent sequences:  A334126 A334127 A334128 * A334130 A334131 A334132 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 14 2020 STATUS approved

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Last modified September 29 20:22 EDT 2020. Contains 337432 sequences. (Running on oeis4.)