A333912 Numbers k such that phi(k) is not the sum of 3 squares, where phi is the Euler totient function (A000010).

29, 58, 61, 77, 93, 99, 113, 122, 124, 141, 145, 154, 157, 169, 186, 188, 198, 226, 232, 237, 241, 253, 282, 287, 290, 301, 305, 314, 316, 317, 325, 338, 348, 349, 363, 369, 381, 385, 387, 413, 429, 441, 449, 465, 474, 482, 484, 488, 493, 495, 496, 506, 508, 509

Offset

1,1

Comments

Pollack (2011) proved that the complementary sequence has asymptotic density 7/8. Therefore the asymptotic density of this sequence is 1/8.

Links

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

Paul Pollack, Values of the Euler and Carmichael functions which are sums of three squares, Integers, Vol. 11 (2011), pp. 145-161.

Example

1 is not a term since phi(1) = 1 = 0^2 + 0^2 + 1^2 is the sum of 3 squares.
29 is a term since phi(29) = 28 is not the sum of 3 squares.

Mathematica

Select[Range[500], SquaresR[3, EulerPhi[#]] == 0 &]

Crossrefs

Cf. A000010, A004215, A039770, A272405, A333909, A333913.

Sequence in context: A340669 A040812 A184081 * A333913 A164011 A048846

Adjacent sequences: A333909 A333910 A333911 * A333913 A333914 A333915

Keyword

nonn

Author

Amiram Eldar, Apr 09 2020

Status

approved