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

1,1

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

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001358.

Sequence in context: A116589 A118688 A118691 * A033476 A183978 A118696

Adjacent sequences: A087715 A087716 A087717 * A087719 A087720 A087721

Keyword

nonn

Author

Reinhard Zumkeller, Sep 29 2003

Status

approved