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A083795
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Numbers n such that n and n-1 have the same number of divisors. Numbers not included in A083794.
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5
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3, 15, 22, 27, 34, 35, 39, 45, 58, 76, 86, 87, 94, 95, 99, 105, 117, 119, 123, 134, 136, 142, 143, 146, 148, 159, 172, 178, 190, 202, 203, 206, 214, 215, 218, 219, 231, 232, 243, 244, 245, 254, 286, 297, 299, 302, 303, 327, 333, 335, 345, 375, 376, 382, 388
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OFFSET
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1,1
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COMMENTS
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Also numbers n such that sigma_0(n+1) * sigma_0(n) / (sigma_0(n+1) + sigma_0(n)) = c, c an integer. - Ctibor O. Zizka, Nov 01 2008
Heath-Brown proved that this sequence is infinite. Hildebrand and Erdős, Pomerance, & Sárközy show that n sqrt(log log n) << a(n) << n (log log n)^3, where << is Vinogradov notation. - Charles R Greathouse IV, Oct 20 2013
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LINKS
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MAPLE
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with(numtheory): for n from 3 to 10^3 do if tau(n) = tau(n-1) then printf(`%d, `, n) fi: od:
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MATHEMATICA
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SequencePosition[DivisorSigma[0, Range[400]], {x_, x_}][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 09 2019 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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