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A248023 Even numbers which are neither primes nor perfect powers and are coprime to the sum of their divisors. 1

%I

%S 50,98,242,338,392,578,722,800,968,1058,1250,1352,1682,1922,2312,2450,

%T 2738,2888,3362,3698,3872,4232,4418,4802,5408,5618,6050,6272,6728,

%U 6962,7442,7688,8450,8978,9248,10082,10658,10952,11552,12482,12800,13448,13778,14450

%N Even numbers which are neither primes nor perfect powers and are coprime to the sum of their divisors.

%H G. C. Greubel, <a href="/A248023/b248023.txt">Table of n, a(n) for n = 1..1500</a>

%e 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.

%t perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; Select[ 2 Range@ 7500, !PrimeQ[ #] && GCD[#, DivisorSigma[1, #]] == 1 && !perfectPowerQ[ #] &]

%o (PARI) lista(nn) = {forstep(n=4, nn, 2, if (!ispower(n) && (gcd(n, sigma(n))==1), print1(n, ", ")););} \\ _Michel Marcus_, Oct 02 2014

%Y Cf. A003624, A106543, A248020.

%K nonn,easy

%O 1,1

%A _Robert G. Wilson v_, Sep 29 2014

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Last modified September 28 04:28 EDT 2022. Contains 357063 sequences. (Running on oeis4.)