A090196 Odd integers with two divisors a, b such that a < b <= 2a.

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

Author

Steven Finch, Jan 22 2004

Keywords

• nonn

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.

Crossrefs

Cf. A000005, A000203, A071562, A082663, A090196, A196020, A236104, A237270, A237271, A237590, A237593, A244579.

Programs

Mathematica

Select[Range[1, 999, 2], (Divisors[#] /. {_, a_, _, b_, _} /; a < b <= 2a -> True) === True&] (* Jean-François Alcover, Nov 05 2016 *)

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

Formula

a(n) ~ 2n. - Charles R Greathouse IV, Jun 20 2013

Extensions

Corrected by Charles R Greathouse IV, Jul 23 2012

Corrected by Jean-François Alcover and Charles R Greathouse IV, Jun 20 2013