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 A188047 Numbers k such that k^k-1 and k^k+1 are squarefree. 1
 2, 4, 6, 12, 16, 20, 22, 34, 36, 42, 52, 56, 58, 60, 66, 72, 78, 84, 86, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 112, 114, 128, 138, 140, 142, 144, 156, 158 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Kevin P. Thompson, May 03 2022: (Start) a(39) >= 160 (160^160-1 is squarefree; 160^160+1 has no known square factors but is not completely factored). 162, 186, 198, and 256 are also terms in this sequence. (End) LINKS Table of n, a(n) for n=1..38. Status of 160^160+1 EXAMPLE 6 is a term since 6^6-1 = 46655 = 5*7*31*43 and 6^6+1 = 46657 = 13*37*97 are both squarefree. MATHEMATICA Select[Range@42, SquareFreeQ[#^#-1]&&SquareFreeQ[#^#+1]&] PROG (PARI) isok(k) = issquarefree(k^k-1) && issquarefree(k^k+1); \\ Michel Marcus, Feb 22 2021 CROSSREFS Intersection of A184966 and A184967. Cf. A005117. Sequence in context: A309096 A019280 A090748 * A032465 A089395 A089699 Adjacent sequences: A188044 A188045 A188046 * A188048 A188049 A188050 KEYWORD nonn,hard,more AUTHOR Vladimir Joseph Stephan Orlovsky, Mar 19 2011 EXTENSIONS a(11)-a(25) from D. S. McNeil, Mar 22 2011 a(26)-a(31) from Amiram Eldar, Feb 22 2021 a(32)-a(38) (from FactorDB) added by Kevin P. Thompson, May 03 2022 STATUS approved

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Last modified March 3 15:08 EST 2024. Contains 370512 sequences. (Running on oeis4.)