OFFSET
1,1
COMMENTS
Numbers of the form sum_{i=j..2k+1} i where j>=1 and 2k+1>j and k>=1. Numbers of the form (2k+1+j)*(2k+2-j)/2, j>=1, k>=1, 2k+1>j. - R. J. Mathar, Dec 04 2011
Subsequences include the A000384 where >=6, the A014106 where >=5, A071355 where >=12, A130861 where >=9, A139577 where >=13, A139579 where >=17 etc. The sequence is the union of all odd-indexed rows of A141419, except its first column and numbers <=3: {5,6}, {9,12,14,15}, {13,18,22,25,27,28}, ... - R. J. Mathar, Dec 04 2011
Does this sequence have asymptotic density 1? - Robert Israel, Nov 27 2018
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
5=2+3, 6=1+2+3, 9=4+5, 12=3+4+5,...
MAPLE
f:= proc(n) local r, k;
for r in select(t -> (2*t-1)^2 >= 1+8*n, numtheory:-divisors(2*n) minus {2*n}) do
k:= (r + 2*n/r - 3)/4;
if k::posint and r >= 2*k+2 then return true fi
od:
false
end proc:
select(f, [$1..1000]); # Robert Israel, Nov 27 2018
MATHEMATICA
z=200; lst1={}; Do[c=a; Do[c+=b; If[c<=2*z, AppendTo[lst1, c]], {b, a-1, 1, -1}], {a, 1, z, 2}]; Union@lst1
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 12 2010
STATUS
approved