A188049 Numbers k such that k^k-1 and k^k+1 are both not squarefree.
17, 18, 19, 40, 49, 51, 53, 55, 69, 82, 89, 91, 97, 99, 117, 118
Offset: 1
Examples
17 is a term since 17^17-1 = 2^4*10949*1749233*2699538733 and 17^17+1 = 2*3^2*45957792327018709121.
Programs
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Mathematica
Select[Range@41,!(SquareFreeQ[#^#-1]||SquareFreeQ[#^#+1])&]
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PARI
isok(k) = ! issquarefree(k^k-1) && ! issquarefree(k^k+1); \\ Michel Marcus, Feb 22 2021
Extensions
a(5)-a(14) from D. S. McNeil, Mar 22 2011
a(15)-a(16) from Amiram Eldar, Feb 22 2021