OFFSET
1,1
COMMENTS
See A066272 for definition of anti-divisor.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..1000
Jon Perry. The Anti-Divisor.
Jon Perry. The Anti-divisor [Cached copy]
Jon Perry. The Anti-divisor: Even More Anti-Divisors [Cached copy]
EXAMPLE
The anti-divisors of 761 are {2, 3, 9, 13, 39, 117, 169, 507} and these sum to 859, a prime, so 761 is in the sequence.
MATHEMATICA
AntiDivisors[n_] := Union[Drop[Drop[Divisors[2*n-1], 1], -1], Map[2*n/#&, Drop[Select[Divisors[2*n], OddQ], 1]], Drop[Drop[Divisors[2*n+1], 1], -1]]; Do[p = Plus @@ AntiDivisors[n]; If[PrimeQ[p], Print[n]], {n, 2, 10^4}]
PROG
(Python)
from sympy import isprime, divisors
A109350 = [n for n in range(1, 10**6) if isprime(sum([2*d for d in divisors(n) if n > 2*d and n%(2*d)] + [d for d in divisors(2*n-1) if n > d >=2 and n%d] + [d for d in divisors(2*n+1) if n > d >=2 and n%d]))]
# Chai Wah Wu, Aug 12 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Ryan Propper, Aug 21 2005
STATUS
approved