A058266 An approximation to sigma_{1/2}(n): floor( sum_{ d divides n } sqrt(d) ).

1, 2, 2, 4, 3, 6, 3, 7, 5, 7, 4, 12, 4, 8, 8, 11, 5, 13, 5, 14, 9, 10, 5, 19, 8, 11, 10, 16, 6, 21, 6, 16, 11, 12, 11, 25, 7, 12, 12, 23, 7, 24, 7, 19, 18, 13, 7, 30, 10, 19, 13, 20, 8, 26, 13, 26, 14, 15, 8, 39, 8, 15, 20, 24, 14, 28, 9, 22, 15, 28, 9, 41, 9

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, A058267, A058268, A078434, A086671.

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)
with(numtheory):seq(floor(sigma[1/2](n)),n=1..80);

Mathematica

f[n_] := Floor@DivisorSigma[1/2, n]; Array[f, 73] (* Robert G. Wilson v, Aug 17 2017*)

PARI

a(n) = floor(sumdiv(n, d, sqrt(d))); \\ Michel Marcus, Aug 17 2017

Formula

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