OFFSET
1,1
COMMENTS
From Robert Israel, May 02 2023: (Start)
Numbers k with odd divisors d_1, d_2 >= 2 such that k + (d_1+1)/2 is odd and
k + (d_2+1)/2 is even.
Contains no primes, powers of 2 or products of a prime and a power of 2.
Contains odd semiprime p*q iff at least one of p and q == 3 (mod 4).
(End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
9 is in the sequence because 2+3+4=9=4+5.
15 is in the sequence because 7+8=15=1+2+3+4+5.
MAPLE
filter:= proc(n) local a, b, x, y, todd, teven;
todd:= false; teven:= false;
for a in select(type, numtheory:-divisors(n), odd) minus {1} do
b:= 2*n/a;
x:= (a+b+1)/2;
if x::odd then todd:= true; if teven then return true fi
else teven:= true; if todd then return true fi
fi od:
false
end proc:
select(filter, [$1..200]); # Robert Israel, May 01 2023
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; z=200; lst2={}; Do[c=a; Do[c+=b; If[c<=2*z, AppendTo[lst2, c]], {b, a-1, 1, -1}], {a, 2, z, 2}]; Intersection[lst1, lst2]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 12 2010
STATUS
approved