A332515 Numbers k such that phi(k) == 8 (mod 12), where phi is the Euler totient function (A000010).

15, 16, 20, 24, 25, 30, 33, 44, 50, 51, 64, 66, 68, 69, 80, 87, 92, 96, 102, 116, 120, 123, 138, 141, 159, 164, 165, 174, 176, 177, 188, 200, 212, 213, 220, 236, 246, 249, 255, 256, 264, 267, 272, 275, 282, 284, 289, 300, 303, 318, 320, 321, 330, 332, 339, 340

Offset

1,1

Comments

Dence and Pomerance showed that the asymptotic number of the terms below x is ~ c2 * x/sqrt(log(x)), where c2 = (sqrt(2*sqrt(3))/(3*Pi)) * c3^(-1/2) * (2*c3 - c4) = 0.3284176245..., 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. Tenebaum (eds.), Analytic and Elementary Number Theory, Developments in Mathematics, Vol. 1, Springer, Boston, MA, 1998, pp. 7-20, alternative link.

Example

25 is a term since phi(25) = 20 == 8 (mod 12).

Mathematica

Select[Range[400], Mod[EulerPhi[#], 12] == 8 &]

Prog

(Magma) [k:k in [1..350]| EulerPhi(k) mod 12 eq 8]; // Marius A. Burtea, Feb 14 2020

Crossrefs

Cf. A000010, A017617, A175646, A332511, A332512, A332513, A332514, A332516.

Sequence in context: A108856 A241750 A039689 * A063530 A160661 A342941

Adjacent sequences: A332512 A332513 A332514 * A332516 A332517 A332518

Keyword

nonn

Author

Amiram Eldar, Feb 14 2020

Status

approved