login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A073092 Number of numbers of the form x^2 + y^2 (0 <= x <= y) less than or equal to n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{k=0..n} A000161(k).

a(n) is asymptotic to Pi*n/8.

EXAMPLE

0^2 + 0^2, 0^2 + 1^2, 1^2 + 1^2 are less than or equal to 2 hence a(2) = 3.

MATHEMATICA

Accumulate @ Table[Length @ PowersRepresentations[n, 2, 2], {n, 0, 100}] (* Amiram Eldar, Mar 08 2020 *)

PROG

(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

def A073092_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

A073092_list = list(islice(A073092_gen(), 30)) # Chai Wah Wu, Sep 08 2022

CROSSREFS

Cf. A000161, A001481.

Cf. A057655.

Sequence in context: A165706 A242453 A241151 * A088023 A324477 A287292

Adjacent sequences: A073089 A073090 A073091 * A073093 A073094 A073095

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Aug 18 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 29 14:44 EST 2023. Contains 359923 sequences. (Running on oeis4.)