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 A248020 Numbers which are coprime to the sum of their divisors, but are neither primes nor perfect powers. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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[ #] &] PROG (PARI) forcomposite(n=1, 1e3, if(gcd(n, sigma(n))==1, if(!ispower(n), print1(n, ", ")))) \\ Felix FrÃ¶hlich, 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

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Last modified June 6 17:33 EDT 2020. Contains 334831 sequences. (Running on oeis4.)