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)).

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

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*ro-a*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