

A087167


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


10




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


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. A077374, A005101, A005835.
Sequence in context: A267462 A256237 A065235 * A259631 A251921 A217604
Adjacent sequences: A087164 A087165 A087166 * A087168 A087169 A087170


KEYWORD

hard,more,nonn,bref


AUTHOR

Farideh Firoozbakht, Oct 19 2003


STATUS

approved



