A067197 Numbers k such that k*(k+1)/2 is not squarefree.

7, 8, 9, 15, 16, 17, 18, 23, 24, 25, 26, 27, 31, 32, 35, 36, 39, 40, 44, 45, 47, 48, 49, 50, 53, 54, 55, 56, 62, 63, 64, 71, 72, 74, 75, 79, 80, 81, 87, 88, 89, 90, 95, 96, 97, 98, 99, 100, 103, 104, 107, 108, 111, 112, 116, 117, 119, 120, 121, 124, 125, 126, 127, 128

Offset: 1

Author

Benoit Cloitre, Feb 19 2002

Keywords

• nonn

Comments

The asymptotic density of this sequence is 1 - (3/2)*A065474 = 0.5160488515... (Granville and Ramaré, 1996). - Amiram Eldar, Mar 02 2021

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Andrew Granville and Olivier Ramaré, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika, Vol. 43, No. 1 (1996), pp. 73-107; alternative link.

Crossrefs

Complement of A215726.

Cf. A000217, A005117, A013929, A065474.

Programs

Mathematica

Select[Range[200],!SquareFreeQ[#(#+1)/2]&] (* Vladimir Joseph Stephan Orlovsky, Mar 30 2011 *)

PARI

isok(k) = !issquarefree(k*(k+1)/2); \\ Michel Marcus, Feb 17 2021