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%I #16 Mar 15 2018 04:17:13
%S 1,3,5,7,9,11,13,14,15,17,19,20,21,23,25,27,29,31,32,33,34,35,37,38,
%T 39,41,43,44,45,47,49,50,51,53,54,55,56,57,59,61,62,63,64,65,67,68,69,
%U 71,73,74,75,76,77,79,81,83,84,85,86,87,89,90,91,92,93,94,95,97,98,99,101
%N Numbers k such that 1 + 2 ... + k divides lcm(1,2,...,k), or, in other words, lcm(1,2,...,k) is a multiple of the k-th triangular number.
%C k(k+1)/2 divides k! if k+1 is not a prime.
%F Union of odd numbers and even numbers j such that j+1 is neither prime nor prime power. - _Vladeta Jovovic_, Mar 30 2003
%t Select[Range[110],Divisible[LCM@@Range[#],(#(#+1))/2]&] (* _Harvey P. Dale_, Jun 04 2012 *)
%o (PARI) isok(k) = !(lcm(vector(k, j, j)) % (k*(k+1)/2)); \\ _Michel Marcus_, Mar 15 2018
%Y Cf. A006134.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Mar 28 2003
%E More terms from _Ray Chandler_, Aug 07 2003
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