A069059 Numbers k such that k and sigma(k) are not relatively prime.

6, 10, 12, 14, 15, 18, 20, 22, 24, 26, 28, 30, 33, 34, 38, 40, 42, 44, 45, 46, 48, 51, 52, 54, 56, 58, 60, 62, 66, 68, 69, 70, 72, 74, 76, 78, 80, 82, 84, 86, 87, 88, 90, 91, 92, 94, 95, 96, 99, 102, 104, 105, 106, 108, 110, 112, 114, 116, 117, 118, 120, 122, 123, 124

Offset: 1

Author

Benoit Cloitre, Apr 04 2002

Keywords

• easy
• nonn

Comments

Complement of A014567(n).

Also, numbers n such that the reduced denominator of Sum_{d|n} 1/d (A017666) is less than n. - Ivan Neretin, Aug 30 2015

The asymptotic density of this sequence is 1 (Dressler, 1974; Luca, 2007). - Amiram Eldar, May 23 2022

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Robert E. Dressler, On a theorem of Niven, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.
• Florian Luca, On the densities of some subsets of integers, Missouri Journal of Mathematical Sciences, Vol. 19, No. 3 (2007), pp. 167-170.

Crossrefs

Cf. A000203, A009194, A014567, A017666.

Programs

Haskell

a069059 n = a069059_list !! (n-1)
a069059_list = filter ((> 1) . a009194) [1..]
-- Reinhard Zumkeller, Mar 23 2013

Maple

select(n -> igcd(n,numtheory:-sigma(n)) > 1, [$1..1000]); # Robert Israel, Sep 01 2015

Mathematica

Select[Range@125, GCD[#, DivisorSigma[1, #]] > 1 &] (* Ivan Neretin, Aug 30 2015 *)

PARI

for(n=1,160,if(gcd(sigma(n),n)>1,print1(n,",")))

Formula

A009194(a(n)) > 1. - Reinhard Zumkeller, Mar 23 2013