A319697 Sum of even squarefree divisors of n.

0, 2, 0, 2, 0, 8, 0, 2, 0, 12, 0, 8, 0, 16, 0, 2, 0, 8, 0, 12, 0, 24, 0, 8, 0, 28, 0, 16, 0, 48, 0, 2, 0, 36, 0, 8, 0, 40, 0, 12, 0, 64, 0, 24, 0, 48, 0, 8, 0, 12, 0, 28, 0, 8, 0, 16, 0, 60, 0, 48, 0, 64, 0, 2, 0, 96, 0, 36, 0, 96, 0, 8, 0, 76, 0, 40, 0, 112, 0, 12, 0, 84, 0, 64, 0, 88, 0, 24, 0, 48, 0, 48, 0, 96

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = Sum_{d|n} A059841(d)*A008966(d)*d.

a(n) = A048250(n) - A206787(n).

From Amiram Eldar, Nov 15 2025: (Start)

Dirichlet g.f.: (zeta(s)*zeta(s-1)/zeta(2*s-2))*(1 - 2^s/(2^s+2)).

Sum_{k=1..n} a(k) ~ n^2 / 6. (End)

Mathematica

Table[Total[Select[Divisors[n], EvenQ[#]&&SquareFreeQ[#]&]], {n, 100}] (* Harvey P. Dale, May 18 2019 *)
f[2, e_] := 2; f[p_, e_] := p + 1; a[n_] := If[OddQ[n], 0, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Jun 30 2022 *)

Prog

(PARI) A319697(n) = sumdiv(n, d, (!(d%2))*issquarefree(d)*d);

Crossrefs

Cf. A048250, A146076, A183063, A206787, A319698.

Sequence in context: A047765 A068463 A099554 * A107729 A363025 A300073

Adjacent sequences: A319694 A319695 A319696 * A319698 A319699 A319700

Keyword

nonn,easy

Author

Antti Karttunen, Oct 31 2018

Status

approved