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A109351
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Numbers whose anti-divisors sum to a perfect cube.
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1
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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
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OFFSET
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1,1
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COMMENTS
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See A066272 for definition of anti-divisor.
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LINKS
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EXAMPLE
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The anti-divisors of 89 = {2, 3, 59} sum to 64, a perfect cube, so 89 is in the sequence.
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MATHEMATICA
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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}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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