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

1,1

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.

Formula

A009194(a(n)) > 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 *)

Prog

(PARI) for(n=1, 160, if(gcd(sigma(n), n)>1, print1(n, ", ")))
(Haskell)
a069059 n = a069059_list !! (n-1)
a069059_list = filter ((> 1) . a009194) [1..]
-- Reinhard Zumkeller, Mar 23 2013

Crossrefs

Cf. A000203, A009194, A014567, A017666.

Sequence in context: A325281 A100658 A182301 * A273157 A139587 A201463

Adjacent sequences: A069056 A069057 A069058 * A069060 A069061 A069062

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 04 2002

Status

approved