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

1,2

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.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A355647 A367585 A164922 * A343027 A145739 A198191

Adjacent sequences: A205520 A205521 A205522 * A205524 A205525 A205526

Keyword

nonn

Author

Jaroslav Krizek, Jan 28 2012

Extensions

Corrected by T. D. Noe, Feb 03 2012

Status

approved