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A090196
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Odd integers with two divisors a, b such that a < b <= 2a.
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5
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15, 35, 45, 63, 75, 77, 91, 99, 105, 117, 135, 143, 153, 165, 175, 187, 189, 195, 209, 221, 225, 231, 245, 247, 255, 273, 285, 297, 299, 315, 323, 325, 345, 351, 357, 375, 385, 391, 399, 405, 425, 429, 435, 437, 441, 455, 459, 465, 475, 483, 493, 495, 513, 525, 527, 539, 551, 555
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OFFSET
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1,1
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COMMENTS
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Clearly all even integers have two such divisors a, b. Consider the set S of all integers satisfying this property. Maier & Tenenbaum proved Erdős' conjecture that S has asymptotic density 1.
Odd numbers k with the property that the number of parts in the symmetric representation of sigma(k) is not equal to the number of divisors of k.
Odd numbers that are not in A244579.
All terms are composites. (End)
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REFERENCES
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R. R. Hall and G. Tenenbaum, Divisors, Cambridge Univ. Press, 1988, pp. 95-99.
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[1, 999, 2], (Divisors[#] /. {___, a_, ___, b_, ___} /; a < b <= 2a -> True) === True&] (* Jean-François Alcover, Nov 05 2016 *)
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PROG
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(PARI) is(n)=my(d=divisors(n)); for(i=2, #d\2+1, if(d[i]<2*d[i-1], return(n%2))); 0 \\ Charles R Greathouse IV, Jun 20 2013
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CROSSREFS
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Cf. A000005, A000203, A071562, A082663, A090196, A196020, A236104, A237270, A237271, A237590, A237593, A244579.
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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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