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A050452
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a(n) = Sum_{d|n, d == 3 (mod 4)} d.
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18
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0, 0, 3, 0, 0, 3, 7, 0, 3, 0, 11, 3, 0, 7, 18, 0, 0, 3, 19, 0, 10, 11, 23, 3, 0, 0, 30, 7, 0, 18, 31, 0, 14, 0, 42, 3, 0, 19, 42, 0, 0, 10, 43, 11, 18, 23, 47, 3, 7, 0, 54, 0, 0, 30, 66, 7, 22, 0, 59, 18, 0, 31, 73, 0, 0, 14, 67, 0, 26, 42, 71, 3, 0, 0, 93, 19, 18
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} (4*k - 1)*x^(4*k-1)/(1 - x^(4*k-1)). - Ilya Gutkovskiy, Mar 21 2017
Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/48 = 0.205616... (A245058). - Amiram Eldar, Nov 26 2023
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MAPLE
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a := 0 ;
for d in numtheory[divisors](n) do
if d mod 4 = 3 then
a := a+d ;
end if;
end do:
a;
end proc:
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MATHEMATICA
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Table[Total[Select[Divisors[n], Mod[#, 4]==3&]], {n, 80}] (* Harvey P. Dale, Jul 07 2013 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, d*((d % 4) == 3)); \\ Amiram Eldar, Nov 26 2023
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CROSSREFS
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Cf. Sum_{d|n, d=k-1 mod k} d: A000593 (k=2), A078182 (k=3), this sequence (k=4).
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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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