login
A226863
Triangular numbers not divisible by lesser triangular numbers > 1.
3
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
1,1
COMMENTS
We may coin them "prime triangulars". Certainly there are an infinity of them.
FORMULA
a(10000) = 1085943106 = A000217(46603).
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 *)
PROG
(PARI) is(n)=fordiv(n, d, if(ispolygonal(d, 3) && d>1 && d<n, return(0))); ispolygonal(n, 3) && n>1 \\ Charles R Greathouse IV, Jul 29 2016
CROSSREFS
Cf. A000217, A137281 (the indices of these triangular numbers).
Sequence in context: A373279 A262724 A059193 * A325793 A325800 A037167
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 20 2013
STATUS
approved