OFFSET
1,1
COMMENTS
Duffinian numbers (A003624) which are not perfect powers (A001597). - Robert G. Wilson v, Oct 02 2014
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
21 is in the sequence since it is neither a prime nor a powerful number and its divisors 1, 3, 7, and 21 sum to 32, which is coprime to 21.
50 is in the sequence since it is neither a prime nor a powerful number and its divisors 1, 2, 5, 10, 25, and 50 sum to 93, which is coprime to 50.
MATHEMATICA
perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; Select[ Range@ 350, !PrimeQ[ #] && GCD[#, DivisorSigma[1, #]] == 1 && !perfectPowerQ[ #] &]
cpQ[n_]:=CoprimeQ[n, DivisorSigma[1, n]]&&!PrimeQ[n]&&GCD@@ FactorInteger[ n][[All, 2]]<2; Select[Range[2, 400], cpQ] (* Harvey P. Dale, Oct 05 2020 *)
PROG
(PARI) forcomposite(n=1, 1e3, if(gcd(n, sigma(n))==1, if(!ispower(n), print1(n, ", ")))) \\ Felix Fröhlich, Oct 25 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Sep 29 2014
STATUS
approved