A087167 Odd numbers such that sigma(n) - 2n = 6.

8925, 32445, 442365

Offset: 1

Author

Farideh Firoozbakht, Oct 19 2003

Keywords

• hard
• more
• nonn
• bref

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

Examples

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

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

• 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.

Crossrefs

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

Programs

Mathematica

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

PARI

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