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A069059
Numbers k such that k and sigma(k) are not relatively prime.
10
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
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
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 04 2002
STATUS
approved