A330701 Numbers k such that psi(phi(k)) = 2 * phi(psi(k)), where psi(k) is the Dedekind psi function (A001615) and phi(k) is the Euler totient function (A000010).

26, 39, 45, 51, 52, 58, 74, 82, 98, 104, 111, 116, 135, 142, 146, 147, 148, 164, 178, 195, 196, 208, 219, 232, 284, 286, 292, 296, 328, 356, 357, 386, 392, 405, 406, 416, 435, 464, 495, 555, 561, 568, 572, 574, 579, 584, 585, 592, 598, 615, 622, 638, 646, 650

Offset: 1

Author

Amiram Eldar, Dec 26 2019

Keywords

• nonn

Comments

Sandor proved that this sequence is infinite.

Examples

			26 is in the sequence since psi(phi(26)) = psi(12) = 24, and 2 * phi(psi(26)) = 2 * phi(42) = 2 * 12 = 24.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Jozsef Sandor, On the composition of some arithmetic functions, II, Journal of Inequalities in Pure and Applied Mathematics, Vol. 6, No. 3 (2005), Article 73.

Crossrefs

Cf. A000010, A001615, A290002.

Programs

Mathematica

psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); Select[Range[1000], psi[EulerPhi[#]] == 2 * EulerPhi[psi[#]] &]