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 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

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