A050452 a(n) = Sum_{d|n, d == 3 (mod 4)} d.

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

Offset: 1

Author

N. J. A. Sloane, Dec 23 1999

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)
• Mariusz Skałba, A Note on Sums of Two Squares and Sum-of-divisors Functions, INTEGERS 20A (2020) A92.

Crossrefs

Cf. A000593, A050449, A001842, A035462, A245058.

Cf. Sum_{d|n, d=k-1 mod k} d: A000593 (k=2), A078182 (k=3), this sequence (k=4).

Programs

Maple

A050452 := proc(n)
        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:
seq(A050452(n),n=1..40) ; # R. J. Mathar, Dec 20 2011

Mathematica

Table[Total[Select[Divisors[n],Mod[#,4]==3&]],{n,80}] (* Harvey P. Dale, Jul 07 2013 *)

PARI

a(n) = sumdiv(n, d, d*((d % 4) == 3)); \\ Amiram Eldar, Nov 26 2023

Formula

a(n) = A000593(n) - A050449(n). - Reinhard Zumkeller, Apr 18 2006

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