OFFSET
1,1
COMMENTS
In general, since n is even, r is always a multiple of s and even if both r and s are divisors of n, the sum t=r+s may not be. For example, if n=144, then r=3, s=12 and t=r+s=15.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n-th number such that n is even, r = number of odd divisors of n, s = number of even divisors of n, t = r+s = number of divisors of n, are all divisors of n and r is odd, s is even.
EXAMPLE
a(1)=36 since r=3(odd), s=6(even) and t=r+s=9 are all divisors.
MAPLE
with(numtheory); T := proc(n::posint) local x, y, S; S:=divisors(n); x:=nops( select(z->type(z, odd), S) ); y:=nops( select(z->type(z, even), S) ); return [x, y] end; RF:=[]: N:=12^6/2: CNT:=12^4: for w to 1 do for k from 1 to N do n:=2*k; if k mod CNT = 0 then print((N-k)/CNT) fi; r:=T(n)[1]; s:=T(n)[2]; t:=r+s; if type(s, even) and type(r, odd) and andmap(z -> n mod z = 0, [r, s, t]) then RF:=[op(RF), n]; print(n, r, s, t); fi; od od; RF;
CROSSREFS
KEYWORD
nonn
AUTHOR
Walter Kehowski, Jun 24 2006
STATUS
approved