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A058267
An approximation to sigma_{1/2}(n): round( Sum_{ d divides n } sqrt(d) ).
4
1, 2, 3, 4, 3, 7, 4, 7, 6, 8, 4, 12, 5, 9, 9, 11, 5, 14, 5, 14, 10, 10, 6, 20, 8, 11, 11, 16, 6, 21, 7, 17, 12, 12, 12, 25, 7, 13, 13, 23, 7, 24, 8, 19, 19, 14, 8, 31, 11, 20, 14, 20, 8, 26, 14, 26, 15, 15, 9, 39, 9, 16, 21, 25, 15, 28, 9, 23, 16, 28, 9, 42, 10
OFFSET
1,2
LINKS
FORMULA
Sum_{k=1..n} a(k) ~ (2/3)*zeta(3/2) * n^(3/2). - Amiram Eldar, Jan 14 2023
MAPLE
map(round @ numtheory:-sigma[1/2], [$1..100]); # Robert Israel, Aug 18 2017
MATHEMATICA
f[n_] := Round@ DivisorSigma[1/2, n]; Array[f, 70] (* Robert G. Wilson v, Aug 17 2017 *)
PROG
(PARI) a(n) = round(sumdiv(n, d, sqrt(d))); \\ Michel Marcus, Aug 17 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 08 2000
STATUS
approved