A230203 Numbers k such that sigma(phi(k)) > k.

5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 26, 27, 29, 31, 33, 35, 37, 38, 39, 41, 43, 45, 47, 49, 51, 52, 53, 55, 56, 57, 59, 61, 62, 63, 65, 67, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 93, 95, 97, 99, 101, 103, 104, 105, 107, 109, 111, 112, 113, 115, 116, 117, 119

Offset: 1

Author

Vladimir Letsko, Oct 11 2013

Keywords

• nonn

Comments

It seems that the odd number k is not in the sequence if and only if k+2 is a Fermat prime (A019434).

Links

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

Crossrefs

Cf. A000010 (phi), A000203 (sigma).

Cf. A230201, A001229, A018784, A019434, A066694, A227011, A227927, A062402, A230203, A018784.

Programs

Maple

for n do if sigma(phi(n))>n then print{n} fi od:

Mathematica

Select[Range[150],DivisorSigma[1,EulerPhi[#]]>#&] (* Harvey P. Dale, Apr 14 2019 *)

PARI

is(k) = sigma(eulerphi(k)) > k; \\ Amiram Eldar, Apr 04 2024