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A373194
Numbers k such that phi(k) is a Lucas number.
1
1, 2, 3, 4, 5, 6, 8, 10, 12, 19, 27, 38, 54, 2049, 2732, 4098, 5779, 11558, 36717, 48956, 73434, 21994424093409, 29325898791212, 43988848186818, 439894502304193355596420713117, 586526003072257807461894284156, 879789004608386711192841426234, 56570478046795035524653081529155199270281, 56570478046795035532692004624509431078281
OFFSET
1,2
LINKS
MATHEMATICA
lucasQ[n_] := Or @@ (IntegerQ[Sqrt[#]] & /@ (5*n^2 + 20*{-1, 1})); Select[Range[10^4], lucasQ[EulerPhi[#]] &] (* Amiram Eldar, May 27 2024 *)
PROG
(Python)
from sympy.ntheory.primetest import is_square
from sympy import totient
islucas = lambda n: is_square(5*n*n - 20) or is_square(5*n*n + 20)
print([n for n in range(1, 10**4) if islucas(totient(n))])
(PARI) isok(k) = islucas(eulerphi(k)); \\ using islucas from A102460 \\ Michel Marcus, May 27 2024
(PARI) \\ read Max Alekseyev's invphi.gp
a373194(uptoNLucas) = my(A=List()); for(n=0, uptoNLucas, my(L = invphi(fibonacci(n+1) + fibonacci(n-1))); if(#L, for(k=1, #L, listput(A, L[k])))); Set(A);
a373194(150) \\ Hugo Pfoertner, Jun 10 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Darío Clavijo, May 27 2024
EXTENSIONS
a(18)-a(21) from Amiram Eldar, May 27 2024
a(22) onwards from Hugo Pfoertner, May 27 2024
STATUS
approved