

A058072


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


7



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
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OFFSET

1,2


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


LINKS



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



