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Numbers k such that k^3 divides 4^(k^2) + 1.
21

%I #14 Jun 08 2021 02:22:56

%S 1,5,205,505,20705,40505,168305,408545,1342505,1660705,2084645,

%T 4091005,10201505,16322105,16750345,16998805,37217545,49985405,

%U 55042705,117165905,135593005,167731205,186678805,210549145,218301905,418261705

%N Numbers k such that k^3 divides 4^(k^2) + 1.

%C 5 divides a(n) for n > 1.

%t Select[Range[5*10^6], Mod[ 4^(#^2)+1, #^3]==0 &] (* _G. C. Greubel_, Jan 17 2018 *)

%Y Cf. A127263, A128677, A128679, A128680, A128681, A128682, A128683, A128684, A128685, A292330.

%K hard,nonn

%O 1,2

%A _Alexander Adamchuk_, Mar 31 2007

%E More terms from _Ryan Propper_, Jan 13 2008