A054030 Sigma(n)/n for n such that sigma(n) is divisible by n.

1, 2, 2, 3, 2, 3, 2, 4, 4, 3, 4, 4, 2, 4, 4, 3, 4, 3, 2, 5, 5, 4, 3, 4, 2, 4, 4, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 5, 4, 4, 2, 5, 4, 5, 6, 5, 5, 5, 5, 5, 5, 6, 5, 5, 4, 5, 6, 5, 4, 4, 5, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 5, 6, 5, 6, 6, 5, 4, 4, 5, 4, 4, 5, 6, 5, 5, 4, 6, 4, 4, 6, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6

Offset

1,2

Comments

The graph supports the conjecture that all numbers except 2 appear only a finite number of times. Sequences A000396, A005820, A027687, A046060 and A046061 give the n for which the abundancy sigma(n)/n is 2, 3, 4, 5 and 6, respectively. See A134639 for the number of n having abundancy greater than 2. - T. D. Noe, Nov 04 2007

Links

T. D. Noe, Table of n, a(n) for n = 1..1600 (using Flammenkamp's data)

Achim Flammenkamp, The Multiply Perfect Numbers Page

Eric Weisstein's World of Mathematics, Abundancy

Formula

a(n) = sigma(A007691(n))/A007691(n)

Maple

with(numtheory): for i while i < 33000 do
if sigma(i) mod i = 0 then print(sigma(i)/i) fi od;

Prog

(PARI) for(n=1, 1e7, if(denominator(k=sigma(n, -1))==1, print1(k", "))) \\ Charles R Greathouse IV, Mar 09 2014

Crossrefs

Cf. A000203, A007691, A054024, A065997, A219545.

Sequence in context: A173908 A329045 A329345 * A336311 A339874 A134740

Adjacent sequences: A054027 A054028 A054029 * A054031 A054032 A054033

Keyword

nonn,easy

Author

Asher Auel, Jan 19 2000

Extensions

More terms from Jud McCranie, Jul 09 2000

More terms from David Wasserman, Jun 28 2004

Status

approved