|
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|