login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A087167 Odd numbers such that sigma(n) - 2n = 6. 12
8925, 32445, 442365 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If m is in this sequence and 5 doesn't divide m then m is an odd Weird number. There are no other terms up to 2*10^9. Jud McCranie wrote: There are no terms between 2*10^9 and 6.5*10^9.

a(4) > 10^12. - Donovan Johnson, Dec 08 2011

a(4) > 10^13. - Giovanni Resta, Mar 29 2013

a(4) > 10^22. - Wenjie Fang, Jun 16 2014

Any term x of this sequence can be combined with any term y of A141548 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

REFERENCES

R. K. Guy, "Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers." B2 in Unsolved Problems in Number Theory, 2nd ed.New York:Springer- Verlag, pp. 45-53, 1994.

LINKS

Table of n, a(n) for n=1..3.

S. Benkoski, Are All Weird Numbers Even?, Problem E2308, Amer. Math. Monthly, 79 (7) (1972), 774.

C. Rivera, Puzzle 233. A little twist.

Eric Weisstein's World of Mathematics, Weird Number

EXAMPLE

a(1)=8925 because sigma(8925)=2*8925+6 and 8925 is the first odd number such that sigma(n)-2n=6.

MATHEMATICA

Do[If[OddQ[n] && DivisorSigma[1, n] - 2n == 6, Print[n]], {n, 2*10^9}]

PROG

(PARI) is(n)=n%2 && sigma(n)==2*n+6 \\ Charles R Greathouse IV, Mar 09 2014

CROSSREFS

Cf. A003380, A077374, A005101, A005835, A141548 (deficiency 6).

Sequence in context: A267462 A256237 A065235 * A290811 A259631 A251921

Adjacent sequences: A087164 A087165 A087166 * A087168 A087169 A087170

KEYWORD

hard,more,nonn,bref

AUTHOR

Farideh Firoozbakht, Oct 19 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 17:04 EST 2022. Contains 358588 sequences. (Running on oeis4.)