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A073092
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Number of numbers of the form x^2 + y^2 (0 <= x <= y) less than or equal to n.
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1
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1, 2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 9, 9, 10, 11, 12, 12, 13, 13, 13, 13, 13, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 20, 21, 21, 21, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 27, 27, 28, 29, 29, 29, 29, 29, 30, 30, 30, 31, 31, 31, 32, 34, 34, 34, 35, 35, 35, 35, 36, 37, 38
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) is asymptotic to Pi*n/8.
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EXAMPLE
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0^2 + 0^2, 0^2 + 1^2, 1^2 + 1^2 are less than or equal to 2 hence a(2) = 3.
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MATHEMATICA
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Accumulate @ Table[Length @ PowersRepresentations[n, 2, 2], {n, 0, 100}] (*Amiram Eldar,Mar 08 2020 *)
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PROG
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(PARI) a(n)=sum(x=0, n, sum(y=0, x, if((sign(x^2+y^2-n)+1)*sign(x^2+y^2-n), 0, 1)))
(Python)
from itertools import count, islice
from math import prod
from sympy import factorint
defA073092_gen(): # generator of terms
yield (c:=1)
for n in count(1):
f = factorint(n)
c += int(not any(e&1 for e in f.values())) + (((m:=prod(1 if p==2 else (e+1 if p&3==1 else (e+1)&1) for p, e in f.items()))+((((~n & n-1).bit_length()&1)<<1)-1 if m&1 else 0))>>1)
yield c
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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