A184967 Numbers k such that k^k+1 is squarefree.

1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 16, 20, 21, 22, 24, 25, 26, 28, 29, 30, 32, 33, 34, 36, 37, 41, 42, 44, 45, 46, 48, 50, 52, 54, 56, 57, 58, 60, 61, 62, 64, 65, 66, 68, 72, 73, 74, 76, 77, 78, 80, 81, 84, 85, 86, 88, 90, 92, 93, 94, 96, 98, 100, 101, 102, 104, 105, 106, 108, 109, 110, 112, 113, 114, 116, 120, 121, 122

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 19 2011

Keywords

• nonn

Comments

5^5+1 = 3126 = 2*3*521.

6^6+1 = 46657 = 13*37*97.

8^8 = 16777217 = 97*257*673.

Crossrefs

Cf. A005117, A014566, A184966.

Programs

Magma

[ n: n in [1..60] | IsSquarefree(n^n+1) ]; // Bruno Berselli, Mar 24 2011

Mathematica

Select[Range@46,SquareFreeQ[#^#+1]&]

PARI

isok(k) = issquarefree(k^k+1); \\ Michel Marcus, Feb 22 2021

Extensions

Extended by Bruno Berselli, Mar 24 2011

a(39)-a(78) from Amiram Eldar, Feb 22 2021