A248023 Even numbers which are neither primes nor perfect powers and are coprime to the sum of their divisors.
50, 98, 242, 338, 392, 578, 722, 800, 968, 1058, 1250, 1352, 1682, 1922, 2312, 2450, 2738, 2888, 3362, 3698, 3872, 4232, 4418, 4802, 5408, 5618, 6050, 6272, 6728, 6962, 7442, 7688, 8450, 8978, 9248, 10082, 10658, 10952, 11552, 12482, 12800, 13448, 13778, 14450
Offset: 1
Examples
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.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1500
Programs
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Mathematica
perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; Select[ 2 Range@ 7500, !PrimeQ[ #] && GCD[#, DivisorSigma[1, #]] == 1 && !perfectPowerQ[ #] &]
-
PARI
lista(nn) = {forstep(n=4, nn, 2, if (!ispower(n) && (gcd(n, sigma(n))==1), print1(n, ", ")););} \\ Michel Marcus, Oct 02 2014