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A050461
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a(n) = Sum_{d|n, n/d=1 mod 4} d^2.
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7
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1, 4, 9, 16, 26, 36, 49, 64, 82, 104, 121, 144, 170, 196, 234, 256, 290, 328, 361, 416, 442, 484, 529, 576, 651, 680, 738, 784, 842, 936, 961, 1024, 1090, 1160, 1274, 1312, 1370, 1444, 1530, 1664, 1682, 1768, 1849, 1936, 2132, 2116, 2209
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OFFSET
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1,2
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COMMENTS
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Not multiplicative: a(3)*a(7) <> a(21), for example. - R. J. Mathar, Dec 20 2011
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = Pi^3/64 + 7*zeta(3)/16 = 1.010372968262... . (End)
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MAPLE
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a := 0 ;
for d in numtheory[divisors](n) do
if (n/d) mod 4 = 1 then
a := a+d^2 ;
end if;
end do:
a;
end proc:
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MATHEMATICA
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a[n_] := DivisorSum[n, Boole[Mod[n/#, 4] == 1]*#^2&]; Array[a, 50] (* Jean-François Alcover, Feb 12 2018 *)
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PROG
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(Haskell)
a050461 n = sum [d ^ 2 | d <- a027750_row n, mod (div n d) 4 == 1]
(PARI) a(n) = sumdiv(n, d, (n/d % 4 == 1) * d^2); \\ Amiram Eldar, Nov 05 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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