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 A037213 #47 Aug 21 2025 09:55:23
%S A037213 0,1,0,0,2,0,0,0,0,3,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,
%T A037213 0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,
%U A037213 0,0,0,0,0,0,0,0,0,0,0,0,0
%N A037213 Expansion of Sum_{n>=0} n*q^(n^2).
%C A037213 Multiplicative with a(p^(2e)) = p^e, a(p^(2e+1)) = 0. - _Mitch Harris_, Jun 09 2005
%C A037213 a(n) is the square root of n if n is square, zero otherwise. - _Carl R. White_, May 23 2009
%C A037213 Möbius transform of A069290(n). - _Wesley Ivan Hurt_, Jul 09 2025
%H A037213 Reinhard Zumkeller, <a href="/A037213/b037213.txt">Table of n, a(n) for n = 0..10000</a>
%F A037213 Dirichlet generating function: zeta(2*s-1). - _Franklin T. Adams-Watters_, Sep 11 2005
%F A037213 a(n) = sqrt(n) * floor( cos^2(Pi * sqrt(n)) ). - _Carl R. White_, May 23 2009
%F A037213 a(n) = A000196(n) * A010052(n). - _Reinhard Zumkeller_, Jan 27 2010
%F A037213 Sum_{k=1..n} a(k) ~ n/2. - _Vaclav Kotesovec_, Aug 19 2021
%F A037213 a(n) = A066839(n) - A070039(n). - _Ridouane Oudra_, Jun 24 2025
%F A037213 a(n) = Sum_{d|n} A069290(d) * mu(n/d). - _Wesley Ivan Hurt_, Jul 09 2025
%t A037213 Table[If[IntegerQ[n^(1/2)], n^(1/2), 0], {n, 0, 100}] (* _Geoffrey Critzer_, Feb 21 2015 *)
%o A037213 (Haskell)
%o A037213 a037213 n = if n == r ^ 2 then r else 0 where r = a000196 n
%o A037213 a037213_list = zipWith (*) a010052_list a000196_list
%o A037213 -- _Reinhard Zumkeller_, Nov 09 2012
%o A037213 (PARI) a(n) = if (issquare(n), sqrtint(n), 0); \\ _Michel Marcus_, Aug 21 2025
%Y A037213 Cf. A000196, A008683 (mu), A010052, A066839, A069290, A070039.
%K A037213 nonn,mult,changed
%O A037213 0,5
%A A037213 _N. J. A. Sloane_