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 A368684 #16 Jan 28 2025 01:43:01
%S A368684 0,1,1,2,1,2,1,3,1,2,1,4,1,2,1,4,1,3,1,4,1,2,1,6,1,2,1,4,1,4,1,5,1,2,
%T A368684 1,6,1,2,1,6,1,4,1,4,1,2,1,8,1,3,1,4,1,4,1,6,1,2,1,8,1,2,1,6,1,4,1,4,
%U A368684 1,4,1,9,1,2,1,4,1,4,1,8,1,2,1,8,1,2,1,6,1,6
%N A368684 Number of partitions of n into 2 parts such that the smaller part divides both n and floor(n/2).
%C A368684 Essentially, A000005 interspersed with 1's [prepend 0].
%C A368684 Number of divisors of A057979(n+1) for n >= 2.
%H A368684 <a href="/index/Par#part">Index entries for sequences related to partitions</a>.
%F A368684 a(n) = A000005(A057979(n+1)) for n >= 2.
%F A368684 a(2n-1) = A060576(n), a(2n) = A000005(n).
%F A368684 a(n) = d(floor((n+1)/2))^((n+1) mod 2), for n >= 2.
%F A368684 a(n) = d( (n+2+(n-2)*(-1)^n)/4 ) for n >= 2.
%F A368684 a(n) = Sum_{k=1..floor(n/2)} c(n/k) * c(floor(n/2)/k), where c(m) = 1 - ceiling(m) + floor(m).
%F A368684 a(n) = A000005(n) - A091954(n), for n > 1. - _Ridouane Oudra_, Jan 18 2025
%F A368684 Sum_{k=1..n} a(k) ~ (log(n/2) + 2*gamma)*n/2, where gamma is Euler's constant (A001620). - _Amiram Eldar_, Jan 28 2025
%p A368684 with(numtheory): 0, seq(2*tau(n) - tau(2*n) + (n mod 2), n=2..100); # _Ridouane Oudra_, Jan 18 2025
%t A368684 Join[{0}, Table[DivisorSigma[0, (n+2+(n-2)*(-1)^n)/4], {n, 2, 100}]]
%o A368684 (PARI) a(n) = if(n == 1, 0, numdiv((n+2+(n-2)*(-1)^n)/4)); \\ _Amiram Eldar_, Jan 28 2025
%Y A368684 Bisections: A060576, A000005.
%Y A368684 Cf. A001620, A057979, A091954.
%K A368684 nonn,easy
%O A368684 1,4
%A A368684 _Wesley Ivan Hurt_, Jan 03 2024