A050449 a(n) = Sum_{d|n, d == 1 (mod 4)} d.

1, 1, 1, 1, 6, 1, 1, 1, 10, 6, 1, 1, 14, 1, 6, 1, 18, 10, 1, 6, 22, 1, 1, 1, 31, 14, 10, 1, 30, 6, 1, 1, 34, 18, 6, 10, 38, 1, 14, 6, 42, 22, 1, 1, 60, 1, 1, 1, 50, 31, 18, 14, 54, 10, 6, 1, 58, 30, 1, 6, 62, 1, 31, 1, 84, 34, 1, 18, 70, 6, 1, 10, 74, 38, 31, 1

Offset

1,5

Comments

Not multiplicative: a(3)*a(7) != a(21), for example. - R. J. Mathar, Dec 20 2011

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Mariusz Skałba, A Note on Sums of Two Squares and Sum-of-divisors Functions, INTEGERS 20A (2020) A92.

Formula

G.f.: Sum_{n>=0} (4*n+1)*x^(4*n+1)/(1-x^(4*n+1)). - Vladeta Jovovic, Nov 14 2002

a(n) = A000593(n) - A050452(n). - Reinhard Zumkeller, Apr 18 2006

G.f.: Sum_{n >= 1} x^n*(1 + 3*x^(4*n))/(1 - x^(4*n))^2. - Peter Bala, Dec 19 2021

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

Maple

A050449 := proc(n)
        a := 0 ;
        for d in numtheory[divisors](n) do
                if d mod 4 = 1 then
                        a := a+d ;
                end if;
        end do:
        a;
end proc:
seq(A050449(n), n=1..40) ; # R. J. Mathar, Dec 20 2011

Mathematica

a[n_] := DivisorSum[n, Boole[Mod[#, 4] == 1]*#&]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 30 2018 *)

Prog

(PARI) a(n) = sumdiv(n, d, d*((d % 4) == 1)); \\ Michel Marcus, Jan 30 2018

Crossrefs

Cf. A000593, A050452, A050460, A001826, A035451, A245058.

Cf. Sum_{d|n, d==1 (mod k)} d: A000593 (k=2), A078181 (k=3), this sequence (k=4), A284097 (k=5), A284098 (k=6), A284099 (k=7), A284100 (k=8).

Sequence in context: A304404 A290480 A183092 * A316623 A108131 A073354

Adjacent sequences: A050446 A050447 A050448 * A050450 A050451 A050452

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 23 1999

Extensions

More terms from Vladeta Jovovic, Nov 14 2002

More terms from Reinhard Zumkeller, Apr 18 2006

Status

approved