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%I #5 Apr 19 2016 01:07:35
%S 1,2,2,4,3,4,3,7,5,6,4,8,4,6,6,11,5,10,5,12,6,8,5,14,8,8,10,12,6,12,6,
%T 16,8,10,9,20,7,10,8,21,7,12,7,16,15,10,7,22,10,16,10,16,8,20,12,21,
%U 10,12,8,24,8,12,15,24,12,16,9,20,10,18,9,35,9,14,16,20,12,16,9,33,19,14
%N SquareRootSigma(n): Floor of sum of square root of divisors of n. If n = Product p_i^r_i then SRSigma(n) = Product Floor[(p_i^(r_i/2+1/2)-1)/(p_i^(1/2)-1)].
%C Whereas A086671 takes the sum of the floor of the square roots of each of the divisors of n and A058266 takes the floor of the product formula, this sequence takes the product of the floor of the individual prime components of the product formula.
%e a(8) = floor((2^((3+1)/2)-1)/2^(1/2)-1)) = floor(3/(sqrt(2)-1)) = floor(3(sqrt(2)+1)) = 7.
%t f[n_] := Block[{pfe = FactorInteger[n]}, Times @@ Floor[((First /@ pfe)^((Last /@ pfe + 1)/2) - 1)/((First /@ pfe)^(1/2) - 1)]]; Table[ f[n], {n, 82}] (* _Robert G. Wilson v_, Jun 08 2005 *)
%Y Cf. A033635, A086671, A058266.
%K nonn,mult
%O 1,2
%A _Yasutoshi Kohmoto_, May 23 2005
%E Edited, corrected and extended by _Robert G. Wilson v_, Jun 08 2005
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