A109350 Numbers whose anti-divisors sum to a prime.

3, 4, 5, 12, 13, 24, 41, 60, 84, 113, 144, 180, 264, 265, 312, 480, 761, 1012, 1104, 1105, 1201, 1405, 1624, 1740, 1741, 1861, 2112, 2113, 3281, 4140, 4141, 5304, 5512, 5724, 5940, 6385, 6612, 7320, 7564, 7565, 8580, 8845, 9385, 9660, 9661, 9941

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

Sequence in context: A235598 A191197 A055493 * A239356 A077034 A076601

Adjacent sequences: A109347 A109348 A109349 * A109351 A109352 A109353

Keyword

nonn

Author

Ryan Propper, Aug 21 2005

Status

approved