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

0,1

Links

Table of n, a(n) for n=0..10.

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