

A332513


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


6



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
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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^21)), 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. 720, 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



