This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000446 Smallest number that is the sum of 2 squares (allowing zeros) in exactly n ways. 8
 0, 25, 325, 1105, 4225, 5525, 203125, 27625, 71825, 138125, 2640625, 160225, 17850625, 1221025, 1795625, 801125, 1650390625, 2082925, 49591064453125, 4005625, 44890625, 2158203125, 30525625, 5928325, 303460625, 53955078125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Ray Chandler, Table of n, a(n) for n = 1..1458 (a(1459) exceeds 1000 digits). G. Xiao, Two squares FORMULA 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. [From Ant King, Oct 07 2010] a(n) = min(A018782(2n-1),A018782(2n)) for n>1. EXAMPLE a(1) = 0 because 0 is the smallest integer which is uniquely a unique sum of two squares, namely 0^2 + 0^2. a(2) = 25 from 25 = 5^2 + 0 ^2 = 3^2 + 4^2. a(3) = 325 from 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2 + 15^2. a(4) = 1105 from 1105 = 4^2 + 33^2 = 9^2 + 32^2 = 12^2 + 31^2 = 23^2 + 24^2. CROSSREFS Cf. A002144, A018782, A054994. See A016032, A093195 and A124980 for other versions. Sequence in context: A020233 A020319 A000448 * A124980 A188355 A243089 Adjacent sequences:  A000443 A000444 A000445 * A000447 A000448 A000449 KEYWORD nonn AUTHOR EXTENSIONS Better description and more terms from David W. Wilson Aug 15 1996. Definition improved by several correspondents, Nov 12 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.