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

Author

Asher Auel, Jan 19 2000

Keywords

• nonn
• easy

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

Crossrefs

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

Programs

Maple

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

PARI

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

Formula

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

Extensions

More terms from Jud McCranie, Jul 09 2000

More terms from David Wasserman, Jun 28 2004