A226863 Triangular numbers not divisible by lesser triangular numbers > 1.

3, 10, 28, 55, 91, 136, 253, 325, 406, 496, 595, 703, 946, 1081, 1225, 1378, 1711, 1891, 2278, 2485, 2701, 2926, 3403, 3655, 3916, 4465, 4753, 5356, 5671, 7021, 7381, 8128, 8515, 8911, 9316, 10153, 10585, 11026, 11476, 12403, 13366, 13861, 14365, 14878, 15931

Offset: 1

Author

Zak Seidov, Jun 20 2013

Keywords

• nonn

Comments

We may coin them "prime triangulars". Certainly there are an infinity of them.

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A137281 (the indices of these triangular numbers).

Programs

Mathematica

nn = 200; tri = Table[n (n + 1)/2, {n, nn}]; t = {}; Do[i = 2; While[i < n && Mod[tri[[n]], tri[[i]]] > 0, i++]; If[i == n, AppendTo[t, tri[[n]]]], {n, nn}]; t (* T. D. Noe, Jun 20 2013 *)

PARI

is(n)=fordiv(n, d, if(ispolygonal(d,3) && d>1 && d1 \\ Charles R Greathouse IV, Jul 29 2016

Formula

a(10000) = 1085943106 = A000217(46603).