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 A305152 #29 Aug 20 2025 10:48:47
%S A305152 1,-1,1,0,1,-2,1,0,2,-2,1,-1,1,-2,2,1,1,-3,1,-1,2,-2,1,0,2,-2,2,-1,1,
%T A305152 -4,1,1,2,-2,2,-1,1,-2,2,0,1,-4,1,-1,3,-2,1,1,2,-3,2,-1,1,-4,2,0,2,-2,
%U A305152 1,-2,1,-2,3,2,2,-4,1,-1,2,-4,1,0,1,-2,3,-1,2,-4,1
%N A305152 Expansion of Sum_{k>0} x^(k^2) / (1 + x^k).
%H A305152 Seiichi Manyama, <a href="/A305152/b305152.txt">Table of n, a(n) for n = 1..5000</a>
%F A305152 a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(d + n/d). - _Ilya Gutkovskiy_, Nov 02 2021
%F A305152 a(n) = (A228441(n) + A010052(n))/2. - _Ridouane Oudra_, Aug 14 2025
%F A305152 a(n) = A010052(n) - A348952(n). - _Ridouane Oudra_, Aug 20 2025
%o A305152 (PARI) {a(n) = polcoeff(sum(k=1, sqrtint(n), x^(k^2)/(1+x^k))+x*O(x^n), n)}
%o A305152 (PARI) a(n) = sumdiv(n, d, if (d <= sqrtint(n), (-1)^(d + n/d))); \\ _Michel Marcus_, Nov 03 2021
%Y A305152 Cf. A038548, A048272, A193773 (odd bisection), A348608, A228441, A010052, A348952.
%K A305152 sign
%O A305152 1,6
%A A305152 _Seiichi Manyama_, May 26 2018