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 A362961 a(n) = Sum_{b=0..floor(sqrt(n)), n-b^2 is square} b. 2
 1, 1, 0, 2, 3, 0, 0, 2, 3, 4, 0, 0, 5, 0, 0, 4, 5, 3, 0, 6, 0, 0, 0, 0, 12, 6, 0, 0, 7, 0, 0, 4, 0, 8, 0, 6, 7, 0, 0, 8, 9, 0, 0, 0, 9, 0, 0, 0, 7, 13, 0, 10, 9, 0, 0, 0, 0, 10, 0, 0, 11, 0, 0, 8, 20, 0, 0, 10, 0, 0, 0, 6, 11, 12, 0, 0, 0, 0, 0, 12, 9, 10, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) = 0 if n in A022544. a(n) > 0 if n in A001481. LINKS Stefano Spezia, Table of n, a(n) for n = 1..10000 MATHEMATICA a[n_]:=Sum[b Boole[IntegerQ[Sqrt[n-b^2]]], {b, 0, Floor[Sqrt[n]]}]; Array[a, 83] (* Stefano Spezia, May 15 2023 *) PROG (Python) from gmpy2 import * a = lambda n: sum([b for b in range(0, isqrt(n) + 1) if is_square(n - (b*b))]) print([a(n) for n in range(1, 84)]) (Python) from sympy import divisors from sympy.solvers.diophantine.diophantine import cornacchia def A362961(n): c = 0 for d in divisors(n): if (k:=d**2)>n: break q, r = divmod(n, k) if not r: c += sum(d*(a[0]+(a[1] if a[0]!=a[1] else 0)) for a in cornacchia(1, 1, q) or []) return c # Chai Wah Wu, May 15 2023 (PARI) a(n) = sum(b=0, sqrtint(n), if (issquare(n-b^2), b)); \\ Michel Marcus, May 16 2023 CROSSREFS Cf. A022544, A001481. Cf. A143574 (sum of b^2), A000925. Sequence in context: A151867 A262563 A170843 * A292596 A011023 A284610 Adjacent sequences: A362958 A362959 A362960 * A362962 A362963 A362964 KEYWORD nonn,look AUTHOR Darío Clavijo, May 10 2023 STATUS approved

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Last modified September 22 08:35 EDT 2023. Contains 365519 sequences. (Running on oeis4.)