login
A067197
Numbers k such that k*(k+1)/2 is not squarefree.
1
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
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.
Sequence in context: A241289 A037369 A076599 * A047523 A108177 A165480
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 19 2002
STATUS
approved