A334129 Numbers that can be written as a product of one or more consecutive triangular numbers.

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

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

Index to sequences related to polygonal numbers

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