A291682 Numbers k such that phi(psi(phi(k))) = psi(phi(psi(k))).

1, 11, 19, 23, 25, 31, 41, 47, 59, 67, 71, 77, 79, 89, 95, 101, 109, 121, 127, 131, 137, 139, 143, 149, 155, 161, 175, 181, 191, 199, 287, 299, 311, 319, 323, 325, 329, 335, 341, 379, 383, 395, 407, 409, 413, 419, 439, 461, 463, 475, 479, 491, 497, 527, 529, 533, 539, 545, 569, 599, 611, 623, 635

Offset: 1

Author

Altug Alkan, Sep 04 2017

Keywords

• nonn
• easy

Comments

Prime terms are 11, 19, 23, 31, 41, 47, 59, 67, 71, 79, 89, 101, 109, 127, 131, ...

Up to 10^9, twin prime pairs in this sequence are (137, 139), (461, 463), (1019, 1021), (1427, 1429), (2969, 2971), (4229, 4231).

Examples

			11 is a term because phi(psi(phi(11))) = psi(phi(psi(11))).
		

Links

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

Crossrefs

Cf. A000010, A001615, A067160, A290002.

Programs

Mathematica

psi[n_] := If[n < 1, 0, n Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]]; fQ[n_] := EulerPhi[psi[EulerPhi[n]]] == psi[EulerPhi[psi[n]]]; Select[Range@635, fQ] (* Robert G. Wilson v, Sep 23 2017 *)

PARI

a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1));
isok(n) = a001615(eulerphi(a001615(n)))==eulerphi(a001615(eulerphi(n))); \\ after Charles R Greathouse IV at A001615