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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)