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

1, 7, 49, 343, 2401, 2653, 16807, 18571, 117649, 129997, 823543, 909979, 1005487, 4941601, 5764801, 6369853, 7038409, 34591207, 40353607, 44588971, 49268863, 236474833, 242138449, 282475249, 312122797, 344882041, 381079573, 1655323831, 1694969143, 1872866779, 1977326743

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Crossrefs

Cf. A074605.

Programs

Mathematica

Select[Range[10^6], Divisible[PowerMod[3, #, #] + PowerMod[4, #, #], #] &] (* Amiram Eldar, Oct 23 2021 *)

PARI

isok(k) = Mod(4, k)^k + Mod(3, k)^k == 0; \\ Michel Marcus, May 16 2022

Python

from itertools import islice, count
def A045584_gen(startvalue=1): # generator of terms >= startvalue
    kstart = max(startvalue,1)
    k3, k4 = 3**kstart, 4**kstart
    for k in count(kstart):
        if (k3+k4) % k == 0:
            yield k
        k3 *= 3
        k4 *= 4
A045584_list = list(islice(A045584_gen(),10)) # Chai Wah Wu, May 16 2022

Extensions

a(28)-a(31) from Amiram Eldar, Oct 23 2021