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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

Complement of A215726.

Cf. A000217, A005117, A013929, A065474.

Sequence in context: A241289 A037369 A076599 * A047523 A108177 A165480

Adjacent sequences: A067194 A067195 A067196 * A067198 A067199 A067200

Keyword

nonn

Author

Benoit Cloitre, Feb 19 2002

Status

approved