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%I #20 Feb 22 2021 04:03:08
%S 17,18,19,40,49,51,53,55,69,82,89,91,97,99,117,118
%N Numbers k such that k^k-1 and k^k+1 are both not squarefree.
%e 17 is a term since 17^17-1 = 2^4*10949*1749233*2699538733 and 17^17+1 = 2*3^2*45957792327018709121.
%t Select[Range@41,!(SquareFreeQ[#^#-1]||SquareFreeQ[#^#+1])&]
%o (PARI) isok(k) = ! issquarefree(k^k-1) && ! issquarefree(k^k+1); \\ _Michel Marcus_, Feb 22 2021
%Y Cf. A005117, A013929, A184966, A184967, A188047.
%K nonn,hard,more
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 19 2011
%E a(5)-a(14) from _D. S. McNeil_, Mar 22 2011
%E a(15)-a(16) from _Amiram Eldar_, Feb 22 2021