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%I #16 Jan 26 2014 15:22:41
%S 1,49,25,121,784,196,33124,4900,4,4356,2304324,213444,2371600,379456,
%T 87616,360000,3802500,562500,100,532900,5456896,767376,5934096,992016,
%U 9947716,1350244,32467204,44100,2414916,10458756,2683044
%N Sequence of distinct least squares such that the arithmetic mean of the first n squares is also a square.
%H Giovanni Resta, <a href="/A236247/b236247.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = A141391(n)^2
%e a(1) = 1.
%e a(2) is the smallest unused square such that (a(2)+a(1))/2 is a square. So, a(2) = 49.
%e a(3) is the smallest unused square such that (a(3)+a(2)+a(1))/3 is a square. So, a(3) = 25.
%e ...and so on.
%o (Python)
%o def Sq(x):
%o ..for n in range(10**15):
%o ....if x == n**2:
%o ......return True
%o ....if x < n**2:
%o ......return False
%o ..return False
%o def SqAve(init):
%o ..print(init)
%o ..lst = []
%o ..lst.append(init)
%o ..n = 1
%o ..while n < 10**9:
%o ....if n**2 not in lst:
%o ......if Sq(((sum(lst)+n**2)/(len(lst)+1))):
%o ........print(n**2)
%o ........lst.append(n**2)
%o ........n = 1
%o ......else:
%o ........n += 1
%o ....else:
%o ......n += 1
%o SqAve(1)
%Y Cf. A019444, A141391.
%K nonn
%O 1,2
%A _Derek Orr_, Jan 20 2014
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