

A205523


Numbers n such that gcd(n, sigma(n)) = sigma(n) (mod n).


6



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
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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: A059041 A129128 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



