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 A361561 #20 Apr 06 2023 13:00:23 %S A361561 0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,2,0,0,0,1,0,1,0,1,0,0, %T A361561 0,1,0,0,0,1,0,1,0,0,0,0,0,2,0,0,0,0,0,1,0,1,0,0,0,2,0,0,0,1,0,1,0,0, %U A361561 0,1,0,2,0,0,0,0,0,0,0,2,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,2,0,0,0,1,0,0,0,1,0 %N A361561 Number of even middle divisors of n, where "middle divisor" means a divisor in the half-open interval [sqrt(n/2), sqrt(n*2)). %C A361561 Number of even divisors of n in the half-open interval [sqrt(n/2), sqrt(n*2)). %C A361561 Also number of even numbers in the n-th row of A299761. %F A361561 a(n) = A067742(n) - A358434(n). %e A361561 For n = 18 the middle divisor of 18 is [3]. There are no even middle divisors of 18 so a(18) = 0. %e A361561 For n = 20 the middle divisors of 20 are [4, 5]. There is only one even middle divisor of 20 so a(20) = 1. %e A361561 For n = 24 the middle divisors of 24 are [4, 6]. There are two even middle divisors of 24 so a(24) = 2. %t A361561 a[n_] := Count[Divisors[n], _?(EvenQ[#] && Sqrt[n/2] <= # < Sqrt[2*n] &)]; Array[a, 100] (* _Amiram Eldar_, Mar 16 2023 *) %o A361561 (PARI) a(n) = sumdiv(n, d, if (!(d%2), (d>=sqrt(n/2)) && (d<sqrt(2*n)))); \\ _Michel Marcus_, Mar 15 2023 %Y A361561 Cf. A067742, A071090, A071562, A183063, A299761, A358434, A361824. %K A361561 nonn %O A361561 1,24 %A A361561 _Omar E. Pol_, Mar 15 2023