

A049532


Numbers k such that k^2 + 1 is not squarefree.


26



7, 18, 32, 38, 41, 43, 57, 68, 70, 82, 93, 99, 107, 117, 118, 132, 143, 157, 168, 182, 193, 207, 218, 232, 239, 243, 251, 257, 268, 282, 293, 307, 318, 327, 332, 343, 357, 368, 378, 382, 393, 407, 408, 418, 432, 437, 443, 457, 468, 482, 493, 500, 507, 515
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OFFSET

1,1


COMMENTS

The sequence is infinite. For instance, it contains all numbers of the form 7 + 25m.  Emmanuel Vantieghem, Oct 25 2016
More generally, the sequence contains all numbers of the form a(n) + (a(n)^2 + 1) * m for even a(n) and a(n) + (a(n)^2 + 1) * m / 2 for odd a(n).  David A. Corneth, Oct 25 2016
The asymptotic density of this sequence is 1  A335963 = 0.1051587754...  Amiram Eldar, Jul 08 2020


LINKS

R. J. Mathar, Table of n, a(n) for n = 1..7999


FORMULA

A059592(a(n)) > 1; A124809(n) = a(n)^2 + 1.  Reinhard Zumkeller, Nov 08 2006


EXAMPLE

a(1) = 7 because 7^2 + 1 = 49 + 1 = 50 is divisible by 25, a square.


MATHEMATICA

n=1; Reap[Do[While[SquareFreeQ[n^2+1], n++]; Sow[n]; n++, {c, 10000}]][[2, 1]] (* Zak Seidov, Feb 24 2011 *)


PROG

(PARI) for(n=1, 1e4, if(!issquarefree(n^2+1), print1(n", "))) \\ Charles R Greathouse IV, Feb 24 2011
(MAGMA) [n: n in [1..6*10^2] not IsSquarefree(n^2+1)]; // Bruno Berselli, Oct 15 2012


CROSSREFS

Cf. A002522, A059592, A124809, A335963.
Sequence in context: A061876 A103571 A103572 * A156619 A033537 A225286
Adjacent sequences: A049529 A049530 A049531 * A049533 A049534 A049535


KEYWORD

nonn


AUTHOR

Labos Elemer


EXTENSIONS

Definition rewritten by Bruno Berselli, Oct 15 2012
Mathematica updated by JeanFrançois Alcover, Jun 19 2013


STATUS

approved



