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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).

%I A137281 #38 Mar 06 2025 11:05:37
%S A137281 2,4,7,10,13,16,22,25,28,31,34,37,43,46,49,52,58,61,67,70,73,76,82,85,
%T A137281 88,94,97,103,106,118,121,127,130,133,136,142,145,148,151,157,163,166,
%U A137281 169,172,178,187,190,193,196,202,205,208,211,214,217,226,229,232,238,241
%N 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).
%C A137281 All terms > 5 in A005383 are here. - _Zak Seidov_, Jun 20 2013
%C A137281 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
%C A137281 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
%H A137281 Zak Seidov, <a href="/A137281/b137281.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%F A137281 n such that A076982(n) = 2. - _T. D. Noe_, Apr 12 2011
%F A137281 A000217(a(n)) = A226863(n). - _Zak Seidov_, Jun 20 2013
%e A137281 T(4)=10 is not divisible by lesser T's 3, 6;
%e A137281 T(7)=28 is not divisible by lesser T's 3, 6, 10, 15, 21.
%t A137281 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 *)
%Y A137281 Cf. A000217, A005383, A076982, A226863.
%K A137281 nonn
%O A137281 1,1
%A A137281 _Zak Seidov_, Mar 14 2008