A332513 Numbers k such that phi(k) == 4 (mod 12), where phi is the Euler totient function (A000010).

5, 8, 10, 12, 17, 29, 32, 34, 40, 41, 48, 53, 55, 58, 60, 75, 82, 85, 88, 89, 100, 101, 106, 110, 113, 115, 125, 128, 132, 136, 137, 145, 149, 150, 160, 170, 173, 178, 184, 187, 192, 197, 202, 204, 205, 226, 230, 232, 233, 235, 240, 250, 253, 257, 265, 269, 274

Offset

1,1

Comments

Dence and Pomerance showed that the asymptotic number of the terms below x is ~ c1 * x/sqrt(log(x)), where c1 = (sqrt(2*sqrt(3))/(3*Pi)) * c3^(-1/2) * (2*c3 + c4) = 0.6109136202..., c3 = Product_{primes p == 2 (mod 3)} (1 + 1/(p^2-1)), and c4 = Product_{primes p == 2 (mod 3)} (1 - 1/(p+1)^2).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Thomas Dence and Carl Pomerance, Euler's function in residue classes, in: K. Alladi, P. D. T. A. Elliott, A. Granville and G. Tenenbaum (eds.), Analytic and Elementary Number Theory, Developments in Mathematics, Vol. 1, Springer, Boston, MA, 1998, pp. 7-20, alternative link.

Example

17 is a term since phi(17) = 16 == 4 (mod 12).

Mathematica

Select[Range[300], Mod[EulerPhi[#], 12] == 4 &]

Prog

(Magma) [k:k in [1..300]| EulerPhi(k) mod 12 eq 4]; // Marius A. Burtea, Feb 14 2020

Crossrefs

Cf. A000010, A017569, A175646, A332511, A332512, A332514, A332515, A332516.

Sequence in context: A050936 A084146 A314380 * A314381 A325180 A087280

Adjacent sequences: A332510 A332511 A332512 * A332514 A332515 A332516

Keyword

nonn

Author

Amiram Eldar, Feb 14 2020

Status

approved