A067709 Numbers k such that phi(2*sigma(k)) = 2*sigma(phi(k)).

2, 4, 16, 18, 64, 100, 450, 516, 1458, 4096, 4624, 13932, 14406, 20124, 21780, 28900, 29262, 29616, 36450, 45996, 62500, 65536, 92778, 95916, 106092, 106308, 114630, 114930, 121872, 125652, 130050, 140130, 145794, 149124, 160986, 179562, 185100

Offset: 1

Author

Benoit Cloitre, Feb 05 2002

Keywords

• nonn

Comments

Every even superperfect number (A019279) is a term of the sequence. - Vladeta Jovovic, Feb 11 2002

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A000203, A019279.

Programs

Maple

with(numtheory); A067709:=n->`if`( phi(2*sigma(n)) = 2*sigma(phi(n)), n, NULL); seq(A067709(n), n=1..200000); # Wesley Ivan Hurt, Apr 07 2014

Mathematica

Select[Range[200000], EulerPhi[2*DivisorSigma[1, #]] == 2*DivisorSigma[1, EulerPhi[#]] &] (* Amiram Eldar, May 13 2022 *)

PARI

isok(k) = eulerphi(2*sigma(k)) == 2*sigma(eulerphi(k)); \\ Michel Marcus, May 13 2022

Extensions

More terms from Vladeta Jovovic, Feb 11 2002