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A109351 Numbers whose anti-divisors sum to a perfect cube. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A055678 A301281 A091793 * A111134 A036898 A053372

Adjacent sequences:  A109348 A109349 A109350 * A109352 A109353 A109354

KEYWORD

nonn

AUTHOR

Ryan Propper, Aug 21 2005

STATUS

approved

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Last modified April 9 17:48 EDT 2020. Contains 333361 sequences. (Running on oeis4.)