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

1,2

Comments

Complement of primes (A000040) with respect to A205523.

Links

Table of n, a(n) for n=1..50.

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

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

Sequence in context: A100715 A352030 A324652 * A094519 A088723 A228870

Adjacent sequences: A205522 A205523 A205524 * A205526 A205527 A205528

Keyword

nonn

Author

Jaroslav Krizek, Jan 28 2012

Extensions

Corrected by T. D. Noe, Feb 03 2012

Status

approved