cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A090196 #41 Apr 27 2022 10:49:32
%S A090196 15,35,45,63,75,77,91,99,105,117,135,143,153,165,175,187,189,195,209,
%T A090196 221,225,231,245,247,255,273,285,297,299,315,323,325,345,351,357,375,
%U A090196 385,391,399,405,425,429,435,437,441,455,459,465,475,483,493,495,513,525,527,539,551,555
%N A090196 Odd integers with two divisors a, b such that a < b <= 2a.
%C A090196 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.
%C A090196 A244579 and the present sequences are complements in the sequence of odd numbers. - _Hartmut F. W. Hoft_, Dec 10 2016
%C A090196 From _Omar E. Pol_, Jan 10 2017: (Start)
%C A090196 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.
%C A090196 Odd numbers that are not in A244579.
%C A090196 All terms are composites. (End)
%C A090196 The subsequence of semiprimes is A082663. - _Bernard Schott_, Apr 17 2022
%D A090196 R. R. Hall and G. Tenenbaum, Divisors, Cambridge Univ. Press, 1988, pp. 95-99.
%H A090196 Charles R Greathouse IV, <a href="/A090196/b090196.txt">Table of n, a(n) for n = 1..10000</a>
%H A090196 H. Maier and G. Tenenbaum, <a href="http://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pdf">On the set of divisors of an integer</a>, Invent. Math. 76 (1984) 121-128.
%F A090196 a(n) ~ 2n. - _Charles R Greathouse IV_, Jun 20 2013
%t A090196 Select[Range[1, 999, 2], (Divisors[#] /. {___, a_, ___, b_, ___} /; a < b <= 2a -> True) === True&] (* _Jean-François Alcover_, Nov 05 2016 *)
%o A090196 (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
%Y A090196 Cf. A000005, A000203, A071562, A082663, A090196, A196020, A236104, A237270, A237271, A237590, A237593, A244579.
%K A090196 nonn
%O A090196 1,1
%A A090196 _Steven Finch_, Jan 22 2004
%E A090196 Corrected by _Charles R Greathouse IV_, Jul 23 2012
%E A090196 Corrected by _Jean-François Alcover_ and _Charles R Greathouse IV_, Jun 20 2013