A081534 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.

1, 3, 5, 7, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 25, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 101

Offset

1,2

Comments

k(k+1)/2 divides k! if k+1 is not a prime.

Links

Table of n, a(n) for n=1..71.

Formula

Union of odd numbers and even numbers j such that j+1 is neither prime nor prime power. - Vladeta Jovovic, Mar 30 2003

Mathematica

Select[Range[110], Divisible[LCM@@Range[#], (#(#+1))/2]&] (* Harvey P. Dale, Jun 04 2012 *)

Prog

(PARI) isok(k) = !(lcm(vector(k, j, j)) % (k*(k+1)/2)); \\ Michel Marcus, Mar 15 2018

Crossrefs

Cf. A006134.

Sequence in context: A329405 A194391 A347468 * A214547 A097218 A196546

Adjacent sequences: A081531 A081532 A081533 * A081535 A081536 A081537

Keyword

nonn

Author

Amarnath Murthy, Mar 28 2003

Extensions

More terms from Ray Chandler, Aug 07 2003

Status

approved