

A188047


Numbers k such that k^k1 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
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OFFSET

1,1


COMMENTS

a(39) >= 160 (160^1601 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



EXAMPLE

6 is a term since 6^61 = 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^k1) && issquarefree(k^k+1); \\ Michel Marcus, Feb 22 2021


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



