

A067085


a(n) = floor(Sum_{k=1..n} 1/k^(1/2)).


2



1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16
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OFFSET

1,3


LINKS



FORMULA

A wellknown inequality is 2*n^1/2  2 < b(n) < 2*n^1/2  1.


EXAMPLE

a(4) = floor(1 + 1/sqrt(2) + 1/sqrt(3) + 1/sqrt(4)) = floor(2.78445705037617328890999314260681) = 2.


MATHEMATICA

Table[ Floor[ Sum[1/k^(1/2), {k, 1, n} ]], {n, 1, 75} ]


PROG

(PARI) { s=0; for (n=1, 1000, s+=1/n^(1/2); write("b067085.txt", n, " ", floor(s)) ) } \\ Harry J. Smith, May 10 2010


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



