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 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 (list; graph; refs; listen; history; text; internal format)
 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: A341008 A103571 A103572 * A156619 A033537 A225286 Adjacent sequences:  A049529 A049530 A049531 * A049533 A049534 A049535 KEYWORD nonn AUTHOR EXTENSIONS Definition rewritten by Bruno Berselli, Oct 15 2012 Mathematica updated by Jean-François Alcover, Jun 19 2013 STATUS approved

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)