A087718 - OEIS

%I #17 Sep 24 2018 16:53:14

%S 4,6,9,15,25,35,49,77,91,121,143,169,187,209,221,247,289,299,323,361,

%T 391,437,493,527,529,551,589,667,703,713,841,851,899,943,961,989,1073,

%U 1147,1189,1247,1271,1333,1363,1369,1457,1517,1537,1591,1643,1681

%N Semiprimes with greater factor less than twice the smaller factor.

%C A084127(a(n)) < A084126(a(n))*2; subsequence of A001358; A001248 is a subsequence.

%C Odd composite integers which do not have a representation as the sum of an even number of consecutive integers. For instance, 27 is not in the sequence because it has a representation as the sum of an even number of consecutive integers (2+3+4+5+6+7). 35 is in the sequence because it does not have such a representation. - _Andrew S. Plewe_, May 14 2007

%C Decker & Moree prove that this sequence has (x log 4)/(log x)^2 + O(x/(log x)^3) members up to x. - _Charles R Greathouse IV_, Jul 07 2016

%H Charles R Greathouse IV, <a href="/A087718/b087718.txt">Table of n, a(n) for n = 1..10000</a>

%H Andreas Decker and Pieter Moree, <a href="http://arxiv.org/abs/0801.1451">Counting RSA-integers</a>, Results in Mathematics 52 (2008), pp. 35-39.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>

%F a(n) ~ kx log^2 x with k = 1/log 4 = 0.7213..., see Decker & Moree. - _Charles R Greathouse IV_, Jul 07 2016

%e 35=5*7 is a term, as 7<5*2=10;

%e 21=3*7 is not a term, as 7>3*2=6.

%t Select[Range[1700],PrimeOmega[#]==2&&(IntegerQ[Sqrt[#]]|| FactorInteger[ #] [[-1,1]] < 2*FactorInteger[#][[1,1]])&] (* _Harvey P. Dale_, Sep 12 2017 *)

%o (PARI) list(lim)=my(v=List()); forprime(p=2, sqrtint(lim\2), forprime(q=2, min(lim\p,2*p), listput(v,p*q))); Set(v) \\ _Charles R Greathouse IV_, Jul 07 2016

%Y Cf. A001358.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Sep 29 2003