A058268 An approximation to sigma_{1/2}(n): ceiling( sum_{d|n} sqrt(d) ).

1, 3, 3, 5, 4, 7, 4, 8, 6, 8, 5, 13, 5, 9, 9, 12, 6, 14, 6, 15, 10, 11, 6, 20, 9, 12, 11, 17, 7, 22, 7, 17, 12, 13, 12, 26, 8, 13, 13, 24, 8, 25, 8, 20, 19, 14, 8, 31, 11, 20, 14, 21, 9, 27, 14, 27, 15, 16, 9, 40, 9, 16, 21, 25, 15, 29, 10, 23, 16, 29, 10, 42

Offset: 1

Author

N. J. A. Sloane, Dec 08 2000

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A001157, A058266, A058267, A078434.

Programs

Maple

with(numtheory); f := proc(n) local d, t1, t2; t2 := 0; t1 := divisors(n); for d in t1 do t2 := t2 + sqrt(d) end do; t2 end proc; # exact value of sigma_{1/2}(n)

Mathematica

a[n_] := Ceiling[DivisorSigma[1/2, n]]; Array[a, 70] (* Amiram Eldar, Jan 14 2023 *)

Formula

Sum_{k=1..n} a(k) ~ (2/3)*zeta(3/2) * n^(3/2). - Amiram Eldar, Jan 14 2023