A357315 Numbers m such that for all k < m, at least one of m*k - 1 and m*k + 1 is squarefree.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 30, 32, 36, 42, 44, 48, 50, 52, 54, 56, 62, 64, 66, 70, 72, 78, 84, 90, 96, 126, 132, 140, 144, 150, 156, 168, 180, 198, 210, 216, 228, 240, 246, 264, 270, 360, 378, 390, 414, 420, 450, 510, 546, 630, 780, 840, 1230, 1470, 1680, 5250
Offset: 1
Keywords
Examples
11 is not in this sequence because 11*5-1=54, 11*5+1=56 are both squareful numbers and 11*9-1=98, 11*9+1=100 are both squareful numbers.
Links
- Sidney Cadot, Table of n, a(n) for n = 1..69
Programs
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Magma
[n: n in [1..2000] | #[k: k in [1..n-1] | not IsSquarefree(n*k-1) and not IsSquarefree(n*k+1)] eq 0];
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Mathematica
q[n_] := AllTrue[Range[n - 1]*n, SquareFreeQ[# - 1] || SquareFreeQ[# + 1] &]; Select[Range[2000], q] (* Amiram Eldar, Oct 20 2022 *)
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PARI
isok(m) = for (k=1, m-1, if (!issquarefree(m*k - 1) && !issquarefree(m*k + 1), return(0));); return(1); \\ Michel Marcus, Oct 20 2022
Extensions
Name edited by Thomas Scheuerle, Oct 20 2022
a(69) from Amiram Eldar, Oct 20 2022
Comments