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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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 14 2020
STATUS
approved