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%I #32 May 28 2014 23:47:21
%S 4,6,10,12,16,20,20,24,26,30,30,42,42,46,46,48,52,52,54,58,58,58,62,
%T 62,68,70,76,76,78,80,80,92,92,96,96,98,98,102,102,106,110,110,110,110
%N Number of points of norm <= n in square lattice which can be built as entire powers of points of the square lattice seen as image of the complex plane C* (excluding (0,0)).
%H Martin Y. Champel, <a href="/A242877/b242877.txt">Table of n, a(n) for n = 1..10000</a>
%e for n=1, a(1)=4 as (1,0),(0,1),(-1,0),(0,-1) are powers of (1,0), (0,-1),(0,1) and (0,1) respectively powered by 2,3,2 and 3.
%e for n=2, a(2)=6 as in addition of the 4 previous points can be found 2 points (0,2) and (0,-2) built as (1,1)^2 and (1,-1)^2.
%e for n=3, a(3)=10 as in addition of the 6 previous points can be found 4 points (2,2), (2,-2), (-2,-2) and (-2,2) built as (-1,1)^3, (-1,-1)^3, (1,-1)^3 and (1,1)^3 respectively.
%o (Python)
%o from math import *
%o i0=complex(1,0)
%o i1=complex(0,1)
%o f0={0,i0,i1,-i0,-i1}
%o def A242877(n):
%o ....if n==0: return 0
%o ....if n==1: return 4
%o ....f0={0,i0,i1,-i0,-i1}
%o ....k=2
%o ....while True:
%o ........ro=n**(1/k)
%o ........if ro<sqrt(1.9999):break
%o ........ro_int = int(ro)
%o ........for a in range(-ro_int,ro_int+1):
%o ............b_max = int(sqrt(ro*ro-a*a))
%o ............for b in range(-b_max,b_max+1):
%o ................c=complex(a,b)
%o ................f0.add(c**k)
%o ........k+=1
%o ....return len(f0)-1
%Y Cf. A000328, A001597, A069623.
%K nonn
%O 1,1
%A _Martin Y. Champel_, May 25 2014
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