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 A270442 Smallest k > 1 such that none of k^2 - 0, k^2 - 1, k^2 - 2,..., k^2 - n are squarefree. 1
 2, 3, 10, 941, 3052, 8173, 35359, 1526009, 30167284, 46952141, 574236841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS EXAMPLE a(0) = 2 because none of 2^2 - 0 = 4 = (2*2) is squarefree; a(1) = 3 because none of 3^2 - 0 = 9 = (3*3), 3^2 - 1 = 8 = (2*2)*2 are squarefree; a(2) = 10 because 10^2 - 0 = 100 = (2*2)*25, 10^2 - 1 = 99 = (3*3)*11, 10^2 - 2 = 98 = (7*7)*2 are squarefree. MATHEMATICA sk[n_]:=Module[{k=2}, While[AnyTrue[k^2-Range[0, n], SquareFreeQ], k++]; k]; Array[sk, 10] (* Requires Mathematica version 10 or later *) (* The program will take a long time to run. *) (* Harvey P. Dale, Jan 10 2021 *) PROG (PARI) isok(k, n) = {for (j=1, n, if (issquarefree(k^2-j), return (0)); ); 1; } a(n) = {my(k = 2); while (! isok(k, n), k++); k; } \\ Michel Marcus, Apr 11 2016 CROSSREFS Cf. A013929, A271817. Sequence in context: A302250 A290638 A330294 * A330581 A184163 A218271 Adjacent sequences:  A270439 A270440 A270441 * A270443 A270444 A270445 KEYWORD nonn,more AUTHOR Juri-Stepan Gerasimov, Apr 09 2016 EXTENSIONS Offset corrected by Michel Marcus, Apr 11 2016 a(8) from Michel Marcus, Apr 11 2016 a(9) from Seiichi Manyama, Sep 08 2018 a(10) from Giovanni Resta, Oct 29 2018 STATUS approved

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Last modified July 25 16:03 EDT 2021. Contains 346291 sequences. (Running on oeis4.)