A205524 -id:A205524 - cp's OEIS frontend

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

Jaroslav Krizek, Jan 28 2012

nonn

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.

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

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

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

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

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

Corrected by T. D. Noe, Feb 03 2012

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

Original entry on oeis.org

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

Jaroslav Krizek, Jan 28 2012

nonn

Complement of primes (A000040) with respect to A205523.

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

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

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

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

Corrected by T. D. Noe, Feb 03 2012

cp's OEIS Frontend

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

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