This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A299480 #38 Mar 23 2019 01:45:13
%S A299480 1,0,1,1,2,0,1,2,2,0,2,2,2,0,1,3,3,0,2,2,2,0,2,4,2,0,2,2,4,0,1,4,2,0,
%T A299480 3,3,2,0,2,4,4,0,2,2,2,0,2,6,3,0,2,2,4,0,2,4,2,0,4,4,2,0,1,5,4,0,2,2,
%U A299480 4,0,3,6,2,0,2,2,4,0,2,6,2,0,4,4,2,0,2,4,6,0,2,2,2,0,2,8,3,0,3,3,4,0,2,4
%N A299480 List of pairs (a,b) where in the n-th pair, a = number of odd divisors of n and b = number of even divisors of n.
%C A299480 Also sequence found by reading in the upper 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 upper part of the diagram equals A001227(n) the number of odd divisors of n. The number of curves that emerge from the same point (n, 0) to the right hand in the upper part of the diagram equals A183063(n) the number of even divisors of n. So the n-th pair is (A001227(n), A183063(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 A299480 The second diagram in the links section shows only the upper part from the first diagram.
%H A299480 Robert Israel, <a href="/A299480/b299480.txt">Table of n, a(n) for n = 1..10000</a>
%H A299480 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 A299480 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv02.jpg">Upper part of the diagram of periodic curves for the number of divisors of n (for n = 1..16)</a>
%F A299480 Pair(a,b) = Pair(A001227(n), A183063(n)).
%F A299480 G.f.: Sum_{n>=1} (x^(2*n-1) + x^(4*n))/(1-x^(4*n)). - _Robert Israel_, Feb 11 2018
%e A299480 Array begins:
%e A299480 n A001227 A183063
%e A299480 1 1 0
%e A299480 2 1 1
%e A299480 3 2 0
%e A299480 4 1 2
%e A299480 5 2 0
%e A299480 6 2 2
%e A299480 7 2 0
%e A299480 8 1 3
%e A299480 9 3 0
%e A299480 10 2 2
%e A299480 11 2 0
%e A299480 12 2 4
%e A299480 ...
%p A299480 f := proc (n) local t; t := numtheory:-tau(n/2^padic:-ordp(n, 2)); t, numtheory:-tau(n)-t end proc:
%p A299480 map(f, [$1..100]); # _Robert Israel_, Feb 11 2018
%t A299480 m = 105; CoefficientList[Sum[(x^(2n-1) + x^(4n))/(1 - x^(4n)), {n, 1, m/2//Ceiling}] + O[x]^m, x] // Rest (* _Jean-François Alcover_, Mar 22 2019, after _Robert Israel_ *)
%Y A299480 Row sums give A000005.
%Y A299480 For another version see A299485.
%Y A299480 Cf. A001227, A027750, A048272, A183063.
%K A299480 nonn,tabf
%O A299480 1,5
%A A299480 _Omar E. Pol_, Feb 10 2018