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A090196
Odd integers with two divisors a, b such that a < b <= 2a.
5
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
OFFSET
1,1
COMMENTS
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.
A244579 and the present sequences are complements in the sequence of odd numbers. - Hartmut F. W. Hoft, Dec 10 2016
From Omar E. Pol, Jan 10 2017: (Start)
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)
The subsequence of semiprimes is A082663. - Bernard Schott, Apr 17 2022
REFERENCES
R. R. Hall and G. Tenenbaum, Divisors, Cambridge Univ. Press, 1988, pp. 95-99.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
H. Maier and G. Tenenbaum, On the set of divisors of an integer, Invent. Math. 76 (1984) 121-128.
FORMULA
a(n) ~ 2n. - Charles R Greathouse IV, Jun 20 2013
MATHEMATICA
Select[Range[1, 999, 2], (Divisors[#] /. {___, a_, ___, b_, ___} /; a < b <= 2a -> True) === True&] (* Jean-François Alcover, Nov 05 2016 *)
PROG
(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
KEYWORD
nonn
AUTHOR
Steven Finch, Jan 22 2004
EXTENSIONS
Corrected by Charles R Greathouse IV, Jul 23 2012
Corrected by Jean-François Alcover and Charles R Greathouse IV, Jun 20 2013
STATUS
approved