A109351 Numbers whose anti-divisors sum to a perfect cube.

2, 8, 9, 89, 96, 204, 224, 296, 541, 576, 1537, 1701, 4496, 6124, 6611, 7685, 7789, 8381, 8741, 9025, 12048, 12105, 12513, 13711, 15924, 16160, 17180, 21486, 21998, 24657, 26264, 26354, 29864, 32477, 43791, 52518, 53662, 54018, 56189, 81281

Offset

1,1

Comments

See A066272 for definition of anti-divisor.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..586

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 89 = {2, 3, 59} sum to 64, a perfect cube, so 89 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[s = Plus @@ AntiDivisors[n]; If[IntegerQ[s^(1/3)], Print[n]], {n, 2, 10^5}]

Prog

(Python)
from sympy import integer_nthroot
from sympy.ntheory.factor_ import antidivisors
A109351_list = [n for n in range(2, 10**4) if integer_nthroot(sum(antidivisors(n)), 3)[1]] # Chai Wah Wu, Jun 13 2015

Crossrefs

Sequence in context: A301281 A091793 A350454 * A111134 A036898 A053372

Adjacent sequences: A109348 A109349 A109350 * A109352 A109353 A109354

Keyword

nonn

Author

Ryan Propper, Aug 21 2005

Status

approved