A068422 Numbers k such that k-phi(k) divides sigma(k).

2, 3, 5, 6, 7, 10, 11, 13, 14, 17, 19, 22, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 53, 58, 59, 61, 62, 67, 71, 73, 74, 79, 82, 83, 86, 89, 94, 97, 99, 101, 103, 106, 107, 109, 113, 118, 122, 127, 131, 134, 137, 139, 142, 146, 149, 151, 157, 158, 163, 166, 167, 168

Offset: 1

Author

Benoit Cloitre, Mar 02 2002

Keywords

• easy
• nonn

Comments

If p is an odd prime, p and 2*p are in the sequence but there are some other kinds of numbers as 99 or 168.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A055164.

Programs

Maple

filter:= proc(n) uses numtheory; type(sigma(n)/(n - phi(n)), integer) end proc:
select(filter, [$2..1000]); # Robert Israel, May 03 2019

Mathematica

Select[Range[2,200],Divisible[DivisorSigma[1,#], #-EulerPhi[#]]&]  (* Harvey P. Dale, Mar 14 2011 *)

PARI

isok(k) = if(k == 1, 0, my(f = factor(k)); !(sigma(f) % (k-eulerphi(f)))); \\ Amiram Eldar, Apr 24 2025