OFFSET
1,2
COMMENTS
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
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. [Ant King, Oct 07 2010]
a(n) = A124980(n) for n > 1. - M. F. Hasler, Jul 07 2024
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.
PROG
CROSSREFS
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