A087718 Semiprimes with greater factor less than twice the smaller factor.

4, 6, 9, 15, 25, 35, 49, 77, 91, 121, 143, 169, 187, 209, 221, 247, 289, 299, 323, 361, 391, 437, 493, 527, 529, 551, 589, 667, 703, 713, 841, 851, 899, 943, 961, 989, 1073, 1147, 1189, 1247, 1271, 1333, 1363, 1369, 1457, 1517, 1537, 1591, 1643, 1681

Offset: 1

Author

Reinhard Zumkeller, Sep 29 2003

Keywords

• nonn

Comments

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

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

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

Examples

			35=5*7 is a term, as 7<5*2=10;
21=3*7 is not a term, as 7>3*2=6.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Andreas Decker and Pieter Moree, Counting RSA-integers, Results in Mathematics 52 (2008), pp. 35-39.
• Eric Weisstein's World of Mathematics, Semiprime

Crossrefs

Cf. A001358.

Programs

Mathematica

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

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

Formula

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