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 A107331 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)]. 0
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE a(8) = floor((2^((3+1)/2)-1)/2^(1/2)-1)) = floor(3/(sqrt(2)-1)) = floor(3(sqrt(2)+1)) = 7. MATHEMATICA 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 *) CROSSREFS Cf. A033635, A086671, A058266. Sequence in context: A224901 A274176 A083742 * A283187 A324391 A087808 Adjacent sequences:  A107328 A107329 A107330 * A107332 A107333 A107334 KEYWORD nonn,mult AUTHOR Yasutoshi Kohmoto, May 23 2005 EXTENSIONS Edited, corrected and extended by Robert G. Wilson v, Jun 08 2005 STATUS approved

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Last modified December 2 15:41 EST 2021. Contains 349445 sequences. (Running on oeis4.)