

A087167


Odd numbers such that sigma(n)  2n = 6.


12




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, QuasiPerfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers." B2 in Unsolved Problems in Number Theory, 2nd ed.New York:Springer Verlag, pp. 4553, 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



