A137281 Numbers k such that T(k) is not divisible by T(i), 1 < i < k, where T(k) = k-th triangular number A000217(k).

2, 4, 7, 10, 13, 16, 22, 25, 28, 31, 34, 37, 43, 46, 49, 52, 58, 61, 67, 70, 73, 76, 82, 85, 88, 94, 97, 103, 106, 118, 121, 127, 130, 133, 136, 142, 145, 148, 151, 157, 163, 166, 169, 172, 178, 187, 190, 193, 196, 202, 205, 208, 211, 214, 217, 226, 229, 232, 238, 241

Offset: 1

Author

Zak Seidov, Mar 14 2008

Keywords

• nonn

Comments

All terms > 5 in A005383 are here. - Zak Seidov, Jun 20 2013

All terms except 2 are congruent to 1 (mod 3). This is required for 3 not to be a divisor of T(n). - Franklin T. Adams-Watters, Dec 10 2019

Conjecture: a(n) ~ C * n * log(n) for some constant C, in analogy with the prime number theorem (see A000040). - Harry Richman, Mar 05 2025

Examples

			T(4)=10 is not divisible by lesser T's 3, 6;
T(7)=28 is not divisible by lesser T's 3, 6, 10, 15, 21.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A000217, A005383, A076982, A226863.

Programs

Mathematica

nn = 241; tri = Table[n*(n+1)/2, {n, nn}]; Select[Range[2, nn], ! MemberQ[Mod[tri[[#]], Take[tri, {2, # - 1}]], 0] &] (* T. D. Noe, Apr 12 2011 *)

Formula

n such that A076982(n) = 2. - T. D. Noe, Apr 12 2011

A000217(a(n)) = A226863(n). - Zak Seidov, Jun 20 2013