A248020 Numbers which are coprime to the sum of their divisors, but are neither primes nor perfect powers.

21, 35, 39, 50, 55, 57, 63, 65, 75, 77, 85, 93, 98, 111, 115, 119, 129, 133, 143, 155, 161, 171, 175, 183, 185, 187, 189, 201, 203, 205, 209, 215, 217, 219, 221, 235, 237, 242, 245, 247, 253, 259, 265, 275, 279, 291, 299, 301, 305, 309, 319, 323, 325, 327, 329, 333, 335, 338, 341

Offset

1,1

Comments

Intersection of A003624 and A106543. - Michel Marcus, Sep 30 2014

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

Sequence in context: A095738 A216467 A330949 * A290435 A138227 A246157

Adjacent sequences: A248017 A248018 A248019 * A248021 A248022 A248023

Keyword

nonn,easy

Author

Robert G. Wilson v, Sep 29 2014

Status

approved