A058268 - OEIS

%I #8 Jan 14 2023 08:45:27

%S 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,

%T 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,

%U 14,27,15,16,9,40,9,16,21,25,15,29,10,23,16,29,10,42

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

%H Amiram Eldar, <a href="/A058268/b058268.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{k=1..n} a(k) ~ (2/3)*zeta(3/2) * n^(3/2). - _Amiram Eldar_, Jan 14 2023

%p 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)

%t a[n_] := Ceiling[DivisorSigma[1/2, n]]; Array[a, 70] (* _Amiram Eldar_, Jan 14 2023 *)

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

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Dec 08 2000