%I #19 Apr 19 2017 09:00:42
%S 21,33,35,39,65,69,75,77,87,91,93,105,129,133,135,141,143,145,147,155,
%T 159,161,165,175,177,183,189,195,203,217,259,261,265,267,273,275,279,
%U 285,287,291,295,297,299,301,303,305,309,315,319,321,325,327,329,339
%N Odd split numbers: have a nontrivial factorization n=ab with a and b coprime, so that L(a) + L(b) <= L(n), where L(x) = A029837(x) = ceiling(log_2(x)).
%C All even numbers are split numbers, except that prime powers -- here powers of 2 -- are by definition excluded.
%C The gaps g(n) = a(n+1) - a(n) are growing up to some local maximum before suddenly dropping down to a very small value and starting a new cycle of growth. The local maxima, distinctly seen as kinks in the graph, are g(1) = 12, g(4) = 26, g(12) = 24, g(30) = 42, g(70) = 48, g(157) = 110, g(348) = 96, g(748) = 160, g(1603) = 192, g(3379) = 446, g(7076) = 384, ... They occur at indices slightly larger than twice the preceding one; every other is of size 6*2^k, k = 1,2,3,... while those in between don't seem to follow a simple pattern and are sometimes larger than the subsequent gap of size 6*2^k. - _M. F. Hasler_, Apr 15 2017
%H Michael De Vlieger, <a href="/A036382/b036382.txt">Table of n, a(n) for n = 1..10000</a>
%e s = 39 is a split number since s = 39 = 3*13, gcd(3,13)=1 and L(3) + L(13) = 2 + 4 = L(39).
%t Select[Range[1, 340, 2], Function[n, Total@ Boole@ Map[And[Total@ Ceiling@ Log2@ # <= Ceiling@ Log2@ n, CoprimeQ @@ #] &, Map[{#, n/#} &, Rest@ Take[#, Ceiling[Length[#]/2]]]] > 0 &@ Divisors@ n]] (* _Michael De Vlieger_, Mar 03 2017 *)
%Y Cf. A029827, A029837, A036378-A036390.
%K nonn
%O 1,1
%A _Labos Elemer_
%E Name corrected by _Michael De Vlieger_, Mar 03 2017