%I #24 May 16 2022 11:12:35

%S 1,7,49,343,2401,2653,16807,18571,117649,129997,823543,909979,1005487,

%T 4941601,5764801,6369853,7038409,34591207,40353607,44588971,49268863,

%U 236474833,242138449,282475249,312122797,344882041,381079573,1655323831,1694969143,1872866779,1977326743

%N Numbers k that divide 4^k + 3^k.

%t Select[Range[10^6], Divisible[PowerMod[3, #, #] + PowerMod[4, #, #], #] &] (* _Amiram Eldar_, Oct 23 2021 *)

%o (Python)

%o from itertools import islice, count

%o def A045584_gen(startvalue=1): # generator of terms >= startvalue

%o kstart = max(startvalue,1)

%o k3, k4 = 3**kstart, 4**kstart

%o for k in count(kstart):

%o if (k3+k4) % k == 0:

%o yield k

%o k3 *= 3

%o k4 *= 4

%o A045584_list = list(islice(A045584_gen(),10)) # _Chai Wah Wu_, May 16 2022

%o (PARI) isok(k) = Mod(4, k)^k + Mod(3, k)^k == 0; \\ _Michel Marcus_, May 16 2022

%Y Cf. A074605.

%K nonn

%O 1,2

%A _David W. Wilson_

%E a(28)-a(31) from _Amiram Eldar_, Oct 23 2021