

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
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OFFSET

1,2


LINKS

Ray Chandler, Table of n, a(n) for n = 1..1458 (a(1459) exceeds 1000 digits).
G. Xiao, Two squares
Index entries for sequences related to sums of squares


FORMULA

An algorithm to compute the nth term of this sequence for n>1: Write each of 2n and 2n1 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(2n1),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

N. J. A. Sloane.


EXTENSIONS

Better description and more terms from David W. Wilson Aug 15 1996.
Definition improved by several correspondents, Nov 12 2007


STATUS

approved



