A270442 Smallest k > 1 such that none of k^2 - 0, k^2 - 1, k^2 - 2,..., k^2 - n are squarefree.

2, 3, 10, 941, 3052, 8173, 35359, 1526009, 30167284, 46952141, 574236841

Offset: 0

Author

Juri-Stepan Gerasimov, Apr 09 2016

Keywords

• nonn
• more

Examples

			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.
		

Crossrefs

Cf. A013929, A271817.

Programs

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 *)

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

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