A093195 - OEIS

%I #29 Apr 19 2019 11:23:12

%S 5,65,325,1105,8125,5525,105625,27625,71825,138125,126953125,160225,

%T 1221025,3453125,1795625,801125,446265625,2082925,41259765625,4005625,

%U 44890625,30525625,30994415283203125,5928325,303460625,53955078125,35409725,100140625

%N Least number which is the sum of two distinct nonzero squares in exactly n ways.

%C An algorithm to compute the n-th term of this sequence: Write each of 2n and 2n+1 as products of their divisors in all possible ways and in decreasing order. For each product, 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 * A002144(2)^a2 * ... * 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 distinct positive squares. [_Ant King_, Dec 14 2009; May 26 2010]

%H Ray Chandler, <a href="/A093195/b093195.txt">Table of n, a(n) for n = 1..1438</a> (a(1439) exceeds 1000 digits).

%F a(n) = min(A018782(2n), A018782(2n+1)).

%o (PARI) b(k)=my(c=0);for(i=1,sqrtint((k-1)\2),if(issquare(k-i^2),c+=1));c \\ A025441

%o for(n=1,10,k=1;while(k,if(b(k)==n,print1(k,", ");break);k+=1)) \\ _Derek Orr_, Mar 20 2019

%Y Cf. A002144, A018782, A054994, A025302-A025311 (first entries).  See A016032, A000446 and A124980 for other versions.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Apr 22 2004

%E More terms from _Ant King_, Dec 14 2009 and Feb 07 2010