A205523 Numbers k such that gcd(k, sigma(k)) == sigma(k) (mod k).

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, 59, 61, 67, 71, 73, 79, 83, 88, 89, 97, 101, 103, 104, 107, 109, 113, 120, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 180, 181, 191, 193, 196, 197, 199

Offset: 1

Author

Jaroslav Krizek, Jan 28 2012

Keywords

• nonn

Comments

Numbers m such that A009194(m) = gcd(m, A000203(m)) = A000203(m) mod m = A054024(m).

Complement of A205524. Union of primes (A000040) and composite numbers from A205525.

Examples

			Number 24 is in sequence because gcd(24, sigma(24)) = (sigma(24)=60) mod 24 = 12.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000040, A009194, A054024, A205524, A205525.

Programs

Mathematica

Select[Range[300], Mod[GCD[#, DivisorSigma[1, #]] - DivisorSigma[1, #], #] == 0 &]

PARI

isok(n) = (gcd(n, sigma(n)) % n) == (sigma(n) % n); \\ Michel Marcus, Dec 22 2017

Extensions

Corrected by T. D. Noe, Feb 03 2012