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A078182
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a(n) = Sum_{d|n, d == 2 (mod 3)} d.
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20
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0, 2, 0, 2, 5, 2, 0, 10, 0, 7, 11, 2, 0, 16, 5, 10, 17, 2, 0, 27, 0, 13, 23, 10, 5, 28, 0, 16, 29, 7, 0, 42, 11, 19, 40, 2, 0, 40, 0, 35, 41, 16, 0, 57, 5, 25, 47, 10, 0, 57, 17, 28, 53, 2, 16, 80, 0, 31, 59, 27, 0, 64, 0, 42, 70, 13, 0, 87, 23, 56, 71, 10, 0, 76, 5, 40, 88, 28, 0, 115
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{n>=0} (3*n+2)*x^(3*n+2)/(1-x^(3*n+2)).
Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/36 = 0.274155... (A353908). - Amiram Eldar, Nov 26 2023
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MAPLE
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a := 0 ;
for d in numtheory[divisors](n) do
if modp(d, 3) =2 then
a :=a+d ;
end if;
end do:
a;
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MATHEMATICA
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a[n_] := Plus @@ Select[Divisors[n], Mod[#, 3] == 2 &]; Array[a, 100] (* Giovanni Resta, May 11 2016 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, d*((d%3) == 2)); \\ Michel Marcus, May 11 2016
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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