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 A067085 a(n) = floor(Sum_{k=1..n} 1/k^(1/2)). 2

%I #10 Dec 20 2015 13:33:08

%S 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,

%T 10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,13,13,13,13,13,

%U 13,13,13,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16,16

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

%H Harry J. Smith, <a href="/A067085/b067085.txt">Table of n, a(n) for n = 1..1000</a>

%F A well-known inequality is 2*n^1/2 - 2 < b(n) < 2*n^1/2 - 1.

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

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

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

%K easy,nonn

%O 1,3

%A _Amarnath Murthy_, Jan 07 2002

%E More terms from _Robert G. Wilson v_, Jan 09 2002

%E Terms added by _Harry J. Smith_, May 10 2010

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Last modified August 14 12:13 EDT 2024. Contains 375164 sequences. (Running on oeis4.)