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A068050 Number of values of k, 1<=k<=n, for which floor(n/k) is prime. 3

%I

%S 0,1,1,1,2,2,3,2,2,4,5,3,4,5,6,5,6,5,6,6,7,9,10,6,7,9,9,9,10,10,11,9,

%T 10,12,14,11,12,13,14,13,14,13,14,14,15,17,18,13,14,16,17,18,19,17,19,

%U 18,19,21,22,18,19,20,21,19,21,22,23,23,24,26,27,21,22,23,24,24,26,27

%N Number of values of k, 1<=k<=n, for which floor(n/k) is prime.

%H Reinhard Zumkeller, <a href="/A068050/b068050.txt">Table of n, a(n) for n = 1..10000</a>

%F If p is a prime other than 3, a(p) = a(p-1) + 1. - _Franklin T. Adams-Watters_, Apr 27 2020

%e a(10) = 4 as floor(10/k) for k = 1 to 10 is 10,5,3,2,2,1,1,1,1,1, respectively; this is prime for k = 2,3,4,5.

%t a[n_] := Length[Select[Table[Floor[n/i], {i, 1, n}], PrimeQ]]

%o (Haskell)

%o a068050 n = length [k | k <- [1..n], a010051 (n `div` k) == 1]

%o -- _Reinhard Zumkeller_, Jan 31 2012

%Y Cf. A067514.

%Y Cf. A010051, A205745.

%K easy,nonn

%O 1,5

%A _Amarnath Murthy_, Feb 12 2002

%E Edited by _Dean Hickerson_, Feb 12 2002

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Last modified July 26 09:58 EDT 2021. Contains 346294 sequences. (Running on oeis4.)