OFFSET
1,1
COMMENTS
If odd m is in this sequence and 5 doesn't divide m, then m is an odd Weird number.
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
For k in A059609, 2^(k-1)*(2^k-7) is a term. - Max Alekseyev, Oct 11 2025
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
Max A. Alekseyev, Computing bounded solutions to linear Diophantine equations with the sum of divisors, arXiv:2601.17832 [math.NT], 2026. See p. 9, Table 1.
Stan Benkoski, Are All Weird Numbers Even?, Problem E2308, Amer. Math. Monthly, 79 (7) (1972), 774.
Wenjie Fang, Searching on the boundary of abundance for odd weird numbers, arXiv:2207.12906 [math.NT], 2022.
Carlos Rivera, Puzzle 233. A little twist, The Prime Puzzles & Problems Connection.
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)=sigma(n)==2*n+6; \\ Charles R Greathouse IV, Mar 09 2014
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Farideh Firoozbakht, Oct 19 2003
EXTENSIONS
"Odd" dropped from the definition and a(4) added by Max Alekseyev, Oct 11 2025
STATUS
approved