

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

Harry J. Smith, Table of n, a(n) for n = 1..1000


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

Sequence in context: A090501 A126848 A232753 * A055086 A001462 A082462
Adjacent sequences: A067082 A067083 A067084 * A067086 A067087 A067088


KEYWORD

easy,nonn


AUTHOR

Amarnath Murthy, Jan 07 2002


EXTENSIONS

More terms from Robert G. Wilson v, Jan 09 2002
Terms added by Harry J. Smith, May 10 2010


STATUS

approved



