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 A000446 #53 Jul 15 2024 23:35:19 %S A000446 0,25,325,1105,4225,5525,203125,27625,71825,138125,2640625,160225, %T A000446 17850625,1221025,1795625,801125,1650390625,2082925,49591064453125, %U A000446 4005625,44890625,2158203125,30525625,5928325,303460625,53955078125 %N A000446 Smallest number that is the sum of 2 squares (allowing zeros) in exactly n ways. %C A000446 Could start with a(0) = 3: the smallest nonnegative integer that can be written as sum of two squares in 0 ways. - _M. F. Hasler_, Jul 05 2024 %H A000446 Ray Chandler, <a href="/A000446/b000446.txt">Table of n, a(n) for n = 1..1458</a> (a(1459) exceeds 1000 digits). %H A000446 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~twosquares.en.html">Two squares</a> %H A000446 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a> %F A000446 An algorithm to compute the n-th term of this sequence for n>1: Write each of 2n and 2n-1 as products of their divisors, in decreasing order and in all possible ways. Equate each divisor in the product to (a1+1)(a2+1)...(ar+1), so that a1>=a2>=a3>=...>=ar, and solve for the ai. Evaluate A002144(1)^a1 x A002144(2)^a2 x ... x A002144(r)^ar for each set of values determined above, then the smaller of these products is the least integer to have precisely n partitions into a sum of two squares. [_Ant King_, Oct 07 2010] %F A000446 a(n) = min(A018782(2n-1), A018782(2n)) for n > 1. %F A000446 a(n) = A124980(n) for n > 1. - _M. F. Hasler_, Jul 07 2024 %e A000446 a(1) = 0 because 0 is the smallest integer which is uniquely a unique sum of two squares, namely 0^2 + 0^2. %e A000446 a(2) = 25 from 25 = 5^2 + 0^2 = 3^2 + 4^2. %e A000446 a(3) = 325 from 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2 + 15^2. %e A000446 a(4) = 1105 from 1105 = 4^2 + 33^2 = 9^2 + 32^2 = 12^2 + 31^2 = 23^2 + 24^2. %o A000446 (PARI) A000446(n)=if(n>1, A124980(n), 0) \\ _M. F. Hasler_, Jul 06 2024 %o A000446 (Python) A000446=lambda n: A124980(n) if n>1 else 0 # _M. F. Hasler_, Jul 07 2024 %Y A000446 Cf. A000448 (similar, but "in at least n ways"). %Y A000446 Cf. A002144, A018782, A054994. %Y A000446 See A016032, A093195 and A124980 for other versions. %K A000446 nonn %O A000446 1,2 %A A000446 _N. J. A. Sloane_ %E A000446 Better description and more terms from _David W. Wilson_, Aug 15 1996 %E A000446 Definition improved by several correspondents, Nov 12 2007