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 A058267 #17 Jan 14 2023 08:45:23 %S A058267 1,2,3,4,3,7,4,7,6,8,4,12,5,9,9,11,5,14,5,14,10,10,6,20,8,11,11,16,6, %T A058267 21,7,17,12,12,12,25,7,13,13,23,7,24,8,19,19,14,8,31,11,20,14,20,8,26, %U A058267 14,26,15,15,9,39,9,16,21,25,15,28,9,23,16,28,9,42,10 %N A058267 An approximation to sigma_{1/2}(n): round( Sum_{ d divides n } sqrt(d) ). %H A058267 Robert Israel, <a href="/A058267/b058267.txt">Table of n, a(n) for n = 1..10000</a> %F A058267 Sum_{k=1..n} a(k) ~ (2/3)*zeta(3/2) * n^(3/2). - _Amiram Eldar_, Jan 14 2023 %p A058267 map(round @ numtheory:-sigma[1/2], [$1..100]); # _Robert Israel_, Aug 18 2017 %t A058267 f[n_] := Round@ DivisorSigma[1/2, n]; Array[f, 70] (* _Robert G. Wilson v_, Aug 17 2017 *) %o A058267 (PARI) a(n) = round(sumdiv(n, d, sqrt(d))); \\ _Michel Marcus_, Aug 17 2017 %Y A058267 Cf. A000203, A001157, A058266, A058268, A078434. %K A058267 nonn %O A058267 1,2 %A A058267 _N. J. A. Sloane_, Dec 08 2000