A088832 Numbers n whose abundance is 4: sigma(n) - 2n = 4.

12, 70, 88, 1888, 4030, 5830, 32128, 521728, 1848964, 8378368, 34359083008, 66072609790, 549753192448, 259708613909470, 2251799645913088

Offset

1,1

Comments

A subset of A045769.

If 2^m-5 is prime then n=2^(m-1)*(2^m-5) is in the sequence (see comment lines of the sequence A088831). 12, 88, 1888, 32128, 521728, 8378368 & 34359083008 are such terms. - Farideh Firoozbakht, Feb 15 2008

a(14) > 10^12. - Donovan Johnson, Dec 08 2011

a(14) > 10^13. - Giovanni Resta, Mar 29 2013

a(16) > 10^18. - Hiroaki Yamanouchi, Aug 23 2018

Any term x of this sequence can be combined with any term y of A125246 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - Timothy L. Tiffin, Sep 13 2016

Links

Table of n, a(n) for n=1..15.

Formula

Solutions to sigma[x]-2x=4

Example

Abundances of terms in A045769: {-5,4,4,4,4,4,4,4,4,4} so A045769[1]=9 is not here.

Mathematica

Do[If[DivisorSigma[1, n]==2n+4, Print[n]], {n, 650000000}] - Farideh Firoozbakht, Feb 15 2008

Prog

(PARI) is(n)=sigma(n)==2*n+4 \\ Charles R Greathouse IV, Feb 21 2017

Crossrefs

Cf. A033880, A045768, A045769, A088830, A059608, A125246 (deficiency 4).

Sequence in context: A101097 A067702 A163193 * A366748 A198311 A060930

Adjacent sequences: A088829 A088830 A088831 * A088833 A088834 A088835

Keyword

nonn,more

Author

Labos Elemer, Oct 28 2003

Extensions

One more terms from Farideh Firoozbakht, Feb 15 2008

a(11)-a(12) from Donovan Johnson, Dec 23 2008

a(13) from Donovan Johnson, Dec 08 2011

a(14)-a(15) from Hiroaki Yamanouchi, Aug 23 2018

Status

approved