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

1,2

Comments

A002961 is a subsequence of this sequence. - Paolo P. Lava, Aug 23 2007

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

Links

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

Example

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

Maple

with(numtheory); P:=proc(n) local a, i; for i from 1 by 1 to n do a:=sigma(i+1)/sigma(i); if trunc(a)=a then print(i); fi; od; end: P(100000); # Paolo P. Lava, Aug 23 2007

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A002961.

Sequence in context: A317154 A283785 A267351 * A027304 A070135 A317037

Adjacent sequences: A058069 A058070 A058071 * A058073 A058074 A058075

Keyword

nonn

Author

Leroy Quet, Nov 11 2000

Extensions

More terms from Benoit Cloitre, Jul 27 2002

Status

approved