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%I #21 Aug 23 2023 08:41:31
%S 1,2,3,5,6,7,11,12,13,17,18,19,20,23,24,28,29,31,37,40,41,43,47,53,56,
%T 59,61,67,71,73,79,83,88,89,97,101,103,104,107,109,113,120,127,131,
%U 137,139,149,151,157,163,167,173,179,180,181,191,193,196,197,199
%N Numbers k such that gcd(k, sigma(k)) == sigma(k) (mod k).
%C Numbers m such that A009194(m) = gcd(m, A000203(m)) = A000203(m) mod m = A054024(m).
%C Complement of A205524. Union of primes (A000040) and composite numbers from A205525.
%H Ivan Neretin, <a href="/A205523/b205523.txt">Table of n, a(n) for n = 1..10000</a>
%e Number 24 is in sequence because gcd(24, sigma(24)) = (sigma(24)=60) mod 24 = 12.
%t Select[Range[300], Mod[GCD[#, DivisorSigma[1, #]] - DivisorSigma[1, #], #] == 0 &]
%o (PARI) isok(n) = (gcd(n, sigma(n)) % n) == (sigma(n) % n); \\ _Michel Marcus_, Dec 22 2017
%Y Cf. A000203, A000040, A009194, A054024, A205524, A205525.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Jan 28 2012
%E Corrected by _T. D. Noe_, Feb 03 2012
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