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%I #25 Mar 02 2021 05:59:54
%S 7,8,9,15,16,17,18,23,24,25,26,27,31,32,35,36,39,40,44,45,47,48,49,50,
%T 53,54,55,56,62,63,64,71,72,74,75,79,80,81,87,88,89,90,95,96,97,98,99,
%U 100,103,104,107,108,111,112,116,117,119,120,121,124,125,126,127,128
%N Numbers k such that k*(k+1)/2 is not squarefree.
%C The asymptotic density of this sequence is 1 - (3/2)*A065474 = 0.5160488515... (Granville and Ramaré, 1996). - _Amiram Eldar_, Mar 02 2021
%H Amiram Eldar, <a href="/A067197/b067197.txt">Table of n, a(n) for n = 1..10000</a>
%H Andrew Granville and Olivier Ramaré, <a href="https://doi.org/10.1112/S0025579300011608">Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients</a>, Mathematika, Vol. 43, No. 1 (1996), pp. 73-107; <a href="https://dms.umontreal.ca/~andrew/PDF/ramare.pdf">alternative link</a>.
%t Select[Range[200],!SquareFreeQ[#(#+1)/2]&] (* _Vladimir Joseph Stephan Orlovsky_, Mar 30 2011 *)
%o (PARI) isok(k) = !issquarefree(k*(k+1)/2); \\ _Michel Marcus_, Feb 17 2021
%Y Complement of A215726.
%Y Cf. A000217, A005117, A013929, A065474.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Feb 19 2002
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