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Numbers k such that k and sigma(k) are not relatively prime.
10

%I #26 May 23 2022 11:46:14

%S 6,10,12,14,15,18,20,22,24,26,28,30,33,34,38,40,42,44,45,46,48,51,52,

%T 54,56,58,60,62,66,68,69,70,72,74,76,78,80,82,84,86,87,88,90,91,92,94,

%U 95,96,99,102,104,105,106,108,110,112,114,116,117,118,120,122,123,124

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

%C Complement of A014567(n).

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

%C The asymptotic density of this sequence is 1 (Dressler, 1974; Luca, 2007). - _Amiram Eldar_, May 23 2022

%H Reinhard Zumkeller, <a href="/A069059/b069059.txt">Table of n, a(n) for n = 1..10000</a>

%H Robert E. Dressler, <a href="https://doi.org/10.4153/CMB-1974-019-5">On a theorem of Niven</a>, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.

%H Florian Luca, <a href="http://projecteuclid.org/euclid.mjms/1316032973">On the densities of some subsets of integers</a>, Missouri Journal of Mathematical Sciences, Vol. 19, No. 3 (2007), pp. 167-170.

%F A009194(a(n)) > 1. - _Reinhard Zumkeller_, Mar 23 2013

%p select(n -> igcd(n,numtheory:-sigma(n)) > 1, [$1..1000]); # _Robert Israel_, Sep 01 2015

%t Select[Range@125, GCD[#, DivisorSigma[1, #]] > 1 &] (* _Ivan Neretin_, Aug 30 2015 *)

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

%o (Haskell)

%o a069059 n = a069059_list !! (n-1)

%o a069059_list = filter ((> 1) . a009194) [1..]

%o -- _Reinhard Zumkeller_, Mar 23 2013

%Y Cf. A000203, A009194, A014567, A017666.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Apr 04 2002