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A045584 Numbers k that divide 4^k + 3^k.

%I A045584 #24 May 16 2022 11:12:35
%S A045584 1,7,49,343,2401,2653,16807,18571,117649,129997,823543,909979,1005487,
%T A045584 4941601,5764801,6369853,7038409,34591207,40353607,44588971,49268863,
%U A045584 236474833,242138449,282475249,312122797,344882041,381079573,1655323831,1694969143,1872866779,1977326743
%N A045584 Numbers k that divide 4^k + 3^k.
%t A045584 Select[Range[10^6], Divisible[PowerMod[3, #, #] + PowerMod[4, #, #], #] &] (* _Amiram Eldar_, Oct 23 2021 *)
%o A045584 (Python)
%o A045584 from itertools import islice, count
%o A045584 def A045584_gen(startvalue=1): # generator of terms >= startvalue
%o A045584     kstart = max(startvalue,1)
%o A045584     k3, k4 = 3**kstart, 4**kstart
%o A045584     for k in count(kstart):
%o A045584         if (k3+k4) % k == 0:
%o A045584             yield k
%o A045584         k3 *= 3
%o A045584         k4 *= 4
%o A045584 A045584_list = list(islice(A045584_gen(),10)) # _Chai Wah Wu_, May 16 2022
%o A045584 (PARI) isok(k) = Mod(4, k)^k + Mod(3, k)^k == 0; \\ _Michel Marcus_, May 16 2022
%Y A045584 Cf. A074605.
%K A045584 nonn
%O A045584 1,2
%A A045584 _David W. Wilson_
%E A045584 a(28)-a(31) from _Amiram Eldar_, Oct 23 2021