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

1,1

Comments

Sandor proved that this sequence is infinite.

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.

Example

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

Mathematica

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

Crossrefs

Cf. A000010, A001615, A290002.

Sequence in context: A039324 A043147 A043927 * A050702 A105997 A354345

Adjacent sequences: A330698 A330699 A330700 * A330702 A330703 A330704

Keyword

nonn

Author

Amiram Eldar, Dec 26 2019

Status

approved