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A271817 Smallest k > 1 such that none of k^2 + 0, k^2 + 1, k^2 + 2,..., k^2 + n are squarefree. 1

%I #14 Apr 15 2016 16:20:01

%S 2,7,32,41,239,13982,240761,240761,26220368,93499279

%N Smallest k > 1 such that none of k^2 + 0, k^2 + 1, k^2 + 2,..., k^2 + n are squarefree.

%C a(10) > 1.2*10^8. - _Giovanni Resta_, Apr 15 2016

%e a(0) = 2 because 2 > 1 and none of 2^2 + 0 = 4 = 2^2 is squarefree,

%e a(1) = 7 because none of 7^2 + 0 = 49 = (7^2), 7^2 + 1 = 50 =(5^2)*2 are squarefree,

%e a(2) = 32 because none of 32^2 + 0 = 1024 = (2^2)*156, 32^2 + 1 = 1025 = (5^2)*41, 32^2 + 2 = 1026 = (3^2)*114 are squarefree.

%o (PARI) isok(k, n) = {for (j=0, n, if (issquarefree(k^2+j), return (0));); 1;}

%o a(n) = {my(k = 2); while (! isok(k, n), k++); k;} \\ _Michel Marcus_, Apr 14 2016

%Y Cf. A013929, A045882, A270442.

%K nonn,more

%O 0,1

%A _Juri-Stepan Gerasimov_, Apr 14 2016

%E a(8)-a(9) from _Giovanni Resta_, Apr 15 2016

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