A230606 Numbers n such that sigma(n) = k*(n+1) for some integer k.

2, 3, 5, 7, 11, 13, 17, 19, 20, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 104, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263

Offset: 1

Author

Jaroslav Krizek, Nov 29 2013

Keywords

• nonn

Comments

Numbers n such that A108775(n) = floor(sigma(n) / n) = sigma(n) mod n = A054024(n).

Union primes (A000040) and composite numbers A045768 (k = 1 for primes p, k = 2 for composite numbers).

Examples

			20 is in sequence because sigma(20) = 42 = 2*21.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203(sigma(n)), A054024 (sigma(n) mod n), A108775.

Cf. A045768 (sigma(n) == 2 (mod n)).

Programs

Mathematica

Select[Range[300],Divisible[DivisorSigma[1,#],#+1]&] (* Harvey P. Dale, May 28 2019 *)

Extensions

Example clarified by Harvey P. Dale, May 28 2019