

A242877


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)).


1



4, 6, 10, 12, 16, 20, 20, 24, 26, 30, 30, 42, 42, 46, 46, 48, 52, 52, 54, 58, 58, 58, 62, 62, 68, 70, 76, 76, 78, 80, 80, 92, 92, 96, 96, 98, 98, 102, 102, 106, 110, 110, 110, 110
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OFFSET

1,1


LINKS

Martin Y. Champel, Table of n, a(n) for n = 1..10000


EXAMPLE

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.
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.
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.


PROG

(Python)
from math import *
i0=complex(1, 0)
i1=complex(0, 1)
f0={0, i0, i1, i0, i1}
def A242877(n):
....if n==0: return 0
....if n==1: return 4
....f0={0, i0, i1, i0, i1}
....k=2
....while True:
........ro=n**(1/k)
........if ro<sqrt(1.9999):break
........ro_int = int(ro)
........for a in range(ro_int, ro_int+1):
............b_max = int(sqrt(ro*roa*a))
............for b in range(b_max, b_max+1):
................c=complex(a, b)
................f0.add(c**k)
........k+=1
....return len(f0)1


CROSSREFS

Cf. A000328, A001597, A069623.
Sequence in context: A156037 A089079 A310579 * A193948 A292794 A108724
Adjacent sequences: A242874 A242875 A242876 * A242878 A242879 A242880


KEYWORD

nonn


AUTHOR

Martin Y. Champel, May 25 2014


STATUS

approved



