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A205525
Nonprime numbers k such that gcd(k, sigma(k)) == sigma(k) (mod k).
2
1, 6, 12, 18, 20, 24, 28, 40, 56, 88, 104, 120, 180, 196, 224, 234, 240, 360, 368, 420, 464, 496, 540, 600, 650, 672, 780, 992, 1080, 1344, 1504, 1872, 1888, 1890, 1952, 2016, 2184, 2352, 2376, 2688, 3192, 3276, 3724, 3744, 4284, 4320, 4680, 5292, 5376, 5624
OFFSET
1,2
COMMENTS
Complement of primes (A000040) with respect to A205523.
EXAMPLE
24 is in the sequence because gcd(24; sigma(24)=60) = (sigma(24)=60) mod 24 = 12.
MATHEMATICA
Select[Range[10000], ! PrimeQ[#] && Mod[GCD[#, DivisorSigma[1, #]] - DivisorSigma[1, #], #] == 0 &] (* T. D. Noe, Feb 03 2012 *)
PROG
(PARI) isok(k) = if (!isprime(k), my(s=sigma(k)); Mod(gcd(k, s), k) == Mod(s, k)); \\ Michel Marcus, Feb 09 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 28 2012
EXTENSIONS
Corrected by T. D. Noe, Feb 03 2012
STATUS
approved