

A087718


Semiprimes with greater factor less than twice the smaller factor.


5



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 RSAintegers, Results in Mathematics 52 (2008), pp. 3539.
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



