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A332515 Numbers k such that phi(k) == 8 (mod 12), where phi is the Euler totient function (A000010). 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 03:15 EDT 2021. Contains 347623 sequences. (Running on oeis4.)