

A069059


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


9



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
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OFFSET

1,1


COMMENTS

Also, numbers n such that the reduced denominator of Sum_{dn} 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. 109110.


FORMULA



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 !! (n1)
a069059_list = filter ((> 1) . a009194) [1..]


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



