A058072 Numbers k such that sigma(k) divides sigma(k+1), where sigma(k) is sum of positive divisors of k.

1, 5, 14, 125, 206, 957, 1253, 1334, 1364, 1634, 1673, 1919, 2685, 2759, 2974, 3127, 4364, 5191, 7615, 11219, 12035, 14841, 18873, 19358, 20145, 24957, 27089, 33998, 36566, 42818, 43817, 47795, 48559, 49955, 50039, 56564, 56975, 58373, 58463

Offset: 1

Author

Leroy Quet, Nov 11 2000

Keywords

• nonn

Comments

The quotient (sigma(k+1)/sigma(k)) is equal to 1, 2, 3, 4 or 5 for the first 5000 terms. - Donovan Johnson, Oct 21 2012

Examples

			5 is included because sigma(5) = 6 divides sigma(6) = 12.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000203, A002961.

Programs

Mathematica

Select[Range[10^5], Divisible[DivisorSigma[1, # + 1], DivisorSigma[1, #]] &] (* Michael De Vlieger, Sep 03 2017 *)

PARI

isok(n) = !(sigma(n+1) % sigma(n)); \\ Michel Marcus, Sep 04 2017

Extensions

More terms from Benoit Cloitre, Jul 27 2002