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

1,1

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

Links

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

Formula

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

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

Example

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.

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 *)

Crossrefs

Cf. A000217, A005383, A076982, A226863.

Sequence in context: A194228 A194236 A127762 * A287420 A003067 A130243

Adjacent sequences: A137278 A137279 A137280 * A137282 A137283 A137284

Keyword

nonn

Author

Zak Seidov, Mar 14 2008

Status

approved