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%I #15 Mar 04 2018 23:13:00
%S 0,1,1,1,0,2,2,1,0,2,2,2,0,2,3,1,0,3,2,2,0,2,4,2,0,2,2,2,0,4,4,1,0,2,
%T 3,3,0,2,4,2,0,4,2,2,0,2,6,2,0,3,2,2,0,4,4,2,0,2,4,4,0,2,5,1,0,4,2,2,
%U 0,4,6,3,0,2,2,2,0,4,6,2,0,2,4,4,0,2,4,2,0,6,2,2,0,2,8,2,0,3,3,3,0,4,4,2
%N List of pairs (a,b) where in the n-th pair, a = number of even divisors of n and b = number of odd divisors of n.
%C Also sequence found by reading in the lower part of the diagram of periodic curves for the number of divisors of n (see the first diagram in the Links section). Explanation: the number of curves that emerge from the point (n, 0) to the left hand in the lower part of the diagram equals A183063(n) the number of even divisors of n. The number of curves that emerge from the same point (n, 0) to the right hand in the lower part of the diagram equals A001227(n) the number of odd divisors of n. So the n-th pair is (A183063(n), A001227(n)). Also the total number of curves that emerges from the same point (n, 0) equals A000005(n), the number of divisors of n. Note that at the point (n, 0) the inflection point of the curve that emerges with diameter k represents the divisor n/k.
%C The second diagram in the links section shows only the lower part from the first diagram, upside down.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv01.jpg">Diagram of periodic curves for the number of divisors of n (for n = 1..16)</a>
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv03.jpg">Lower part upside down of the diagram of periodic curves for the number of divisors of n (for n = 1..16)</a>
%F Pair(a,b) = Pair(A183063(n), A001227(n)).
%e Array begins:
%e n A183063 A001227
%e 1 0 1
%e 2 1 1
%e 3 0 2
%e 4 2 1
%e 5 0 2
%e 6 2 2
%e 7 0 2
%e 8 3 1
%e 9 0 3
%e 10 2 2
%e 11 0 2
%e 12 4 2
%e ...
%t Array[{#2, #1 - #2} & @@ {DivisorSigma[0, #], DivisorSum[#, 1 &, EvenQ]} &, 52] // Flatten (* _Michael De Vlieger_, Mar 04 2018 *)
%Y Another version of A299480.
%Y Row sums give A000005.
%Y Cf. A001227, A027750, A048272, A183063.
%K nonn,tabf
%O 1,6
%A _Omar E. Pol_, Mar 03 2018