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

Author

Antti Karttunen, Oct 31 2018

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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

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