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 A107331 #12 Jan 18 2025 19:31:01
%S A107331 1,2,2,4,3,4,3,7,5,6,4,8,4,6,6,11,5,10,5,12,6,8,5,14,8,8,10,12,6,12,6,
%T A107331 16,8,10,9,20,7,10,8,21,7,12,7,16,15,10,7,22,10,16,10,16,8,20,12,21,
%U A107331 10,12,8,24,8,12,15,24,12,16,9,20,10,18,9,35,9,14,16,20,12,16,9,33,19,14
%N A107331 An approximation to sigma_{1/2}(n): multiplicative with a(p^e) = floor((p^(e/2+1/2)-1)/(p^(1/2)-1)) for prime p.
%C A107331 Whereas A086671 takes the sum of the floor of the square roots of each of the divisors of n and A058266 takes the floor of the product formula, this sequence takes the product of the floor of the individual prime components of the product formula.
%e A107331 a(8) = floor((2^((3+1)/2)-1)/(2^(1/2)-1)) = floor(3/(sqrt(2)-1)) = floor(7.242...) = 7.
%t A107331 f[n_] := Block[{pfe = FactorInteger[n]}, Times @@ Floor[((First /@ pfe)^((Last /@ pfe + 1)/2) - 1)/((First /@ pfe)^(1/2) - 1)]]; Table[ f[n], {n, 82}] (* _Robert G. Wilson v_, Jun 08 2005 *)
%Y A107331 Cf. A033635, A086671, A058266.
%K A107331 nonn,mult
%O A107331 1,2
%A A107331 _Yasutoshi Kohmoto_, May 23 2005
%E A107331 Edited, corrected and extended by _Robert G. Wilson v_, Jun 08 2005