A049532 Numbers k such that k^2 + 1 is not squarefree.

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

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: A103571 A365414 A103572 * A156619 A033537 A352741

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 Jean-François Alcover, Jun 19 2013

Status

approved