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 A185373 #14 Mar 20 2025 03:36:57
%S A185373 1,1,1,1,0,1,4,1,5,1,1,1,1,3,1,1,1,1,1,7,5,1,2,1,2,9,3,1,1,1,4,11,11,
%T A185373 25,2,1,1,9,2,1,11,1,4,3,7,1,2,1,2,1,13,1,3,1,13,49,17,1,0,1,1,49,16,
%U A185373 25,1,1,17,19,35,1,14,1,2
%N A185373 The numerator of the fraction |n^2/A049417(n)-A064380(n)|.
%C A185373 n^2/A049417(n) is a multiplicative function, whereas A064380 is not. This sequence here measures the (small) differences n^2/A049417(n)-A064380(n) = 1/3, 1/4, 1/5, 1/6, 0, 1/8, 4/15, 1/10, 5/9, 1/12, 1/5 ...
%H A185373 Amiram Eldar, <a href="/A185373/b185373.txt">Table of n, a(n) for n = 2..10000</a>
%t A185373 f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); isigma[1] = 1; isigma[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) + 1);
%t A185373 infCoprimeQ[n1_, n2_] := Module[{g = GCD[n1, n2]}, If[g == 1, True, AllTrue[ FactorInteger[g][[;; , 1]], BitAnd @@ IntegerExponent[{n1, n2}, #] == 0 &]]];
%t A185373 a[n_] := Abs[Numerator[n^2 / isigma[n] - Sum[Boole[infCoprimeQ[j, n]], {j, 1, n-1}]]]; Array[a, 100, 2] (* _Amiram Eldar_, Mar 20 2025 *)
%Y A185373 Cf. A064380, A049417, A185383 (denominators)
%K A185373 nonn,frac,less
%O A185373 2,7
%A A185373 _Vladimir Shevelev_, Feb 17 2011