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 A366979 #13 Nov 12 2023 13:28:27 %S A366979 1,2,1,2,1,3,1,3,2,2,1,5,1,2,2,3,1,4,1,4,2,2,1,6,1,2,2,3,1,5,1,3,2,2, %T A366979 1,6,1,2,2,5,1,5,1,3,3,2,1,6,1,3,2,3,1,4,1,5,2,2,1,8,1,2,2,3,1,4,1,3, %U A366979 2,4,1,8,1,2,3,3,1,4,1,6,2,2,1,7,1,2,2,4,1,7 %N A366979 Number of divisors of n less than or equal to d(n). %C A366979 First differs from A126131 at a(25) = 1. %F A366979 a(n) = Sum_{d|n, d <= d(n)} 1. %F A366979 a(n) = 1 + Sum_{d|n} (Sum_{i=2..d(n)} ( sign(floor(i/d)) - sign(floor((i-1)/d)) )), where d(n) is the number of divisors of n (A000005). %e A366979 a(8) = 3; There are 3 divisors of 8 that are <= d(8) = 4. They are: {1,2,4}. %e A366979 a(25) = 1; 1 is the only divisor of 25 that is <= d(25) = 3. %t A366979 Table[1 + Sum[Sum[(Sign[Floor[i/k]] - Sign[Floor[(i - 1)/k]]), {i, 2, DivisorSigma[0, n]}] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}] %o A366979 (PARI) a(n) = my(nd=numdiv(n)); sumdiv(n, d, d <= nd); \\ _Michel Marcus_, Oct 30 2023 %Y A366979 Cf. A000005, A126131. %K A366979 nonn,easy %O A366979 1,2 %A A366979 _Wesley Ivan Hurt_, Oct 30 2023