cp's OEIS Frontend

A299485 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.

%I A299485 #15 Mar 04 2018 23:13:00
%S A299485 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 A299485 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 A299485 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 A299485 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 A299485 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 A299485 The second diagram in the links section shows only the lower part from the first diagram, upside down.
%H A299485 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 A299485 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 A299485 Pair(a,b) = Pair(A183063(n), A001227(n)).
%e A299485 Array begins:
%e A299485 n      A183063  A001227
%e A299485 1         0        1
%e A299485 2         1        1
%e A299485 3         0        2
%e A299485 4         2        1
%e A299485 5         0        2
%e A299485 6         2        2
%e A299485 7         0        2
%e A299485 8         3        1
%e A299485 9         0        3
%e A299485 10        2        2
%e A299485 11        0        2
%e A299485 12        4        2
%e A299485 ...
%t A299485 Array[{#2, #1 - #2} & @@ {DivisorSigma[0, #], DivisorSum[#, 1 &, EvenQ]} &, 52] // Flatten (* _Michael De Vlieger_, Mar 04 2018 *)
%Y A299485 Another version of A299480.
%Y A299485 Row sums give A000005.
%Y A299485 Cf. A001227, A027750, A048272, A183063.
%K A299485 nonn,tabf
%O A299485 1,6
%A A299485 _Omar E. Pol_, Mar 03 2018