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%I #20 Jan 14 2023 08:45:19
%S 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,
%T 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,
%U 13,26,14,15,8,39,8,15,20,24,14,28,9,22,15,28,9,41,9
%N An approximation to sigma_{1/2}(n): floor( sum_{ d divides n } sqrt(d) ).
%H Amiram Eldar, <a href="/A058266/b058266.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)
%p with(numtheory):seq(floor(sigma[1/2](n)),n=1..80);
%t f[n_] := Floor@DivisorSigma[1/2, n]; Array[f, 73] (* _Robert G. Wilson v_, Aug 17 2017*)
%o (PARI) a(n) = floor(sumdiv(n, d, sqrt(d))); \\ _Michel Marcus_, Aug 17 2017
%Y Cf. A000203, A001157, A058267, A058268, A078434, A086671.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Dec 08 2000
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