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

Author

Amiram Eldar, Apr 09 2020

Keywords

• nonn

Comments

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

Examples

			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.
		

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.

Crossrefs

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

Programs

Mathematica

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