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
Keywords
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
Programs
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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 *) -
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