A205525 Nonprime numbers k such that gcd(k, sigma(k)) == sigma(k) (mod k).

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

Author

Jaroslav Krizek, Jan 28 2012

Keywords

• nonn

Comments

Complement of primes (A000040) with respect to A205523.

Examples

			24 is in the sequence because gcd(24; sigma(24)=60) = (sigma(24)=60) mod 24 = 12.
		

Crossrefs

Cf. A000203, A000040, A009194, A054024, A205524, A205523.

Programs

Mathematica

Select[Range[10000], ! PrimeQ[#] && Mod[GCD[#, DivisorSigma[1, #]] - DivisorSigma[1, #], #] == 0 &] (* T. D. Noe, Feb 03 2012 *)

PARI

isok(k) = if (!isprime(k), my(s=sigma(k)); Mod(gcd(k, s), k) == Mod(s, k)); \\ Michel Marcus, Feb 09 2021

Extensions

Corrected by T. D. Noe, Feb 03 2012