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%I #43 Nov 19 2022 14:40:12
%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>
%H Randell Heyman, <a href="https://arxiv.org/abs/2111.00408">Primes in floor function sets</a>, arXiv:2111.00408 [math.NT], 2021.
%F If p is a prime other than 3, a(p) = a(p-1) + 1. - _Franklin T. Adams-Watters_, Apr 27 2020
%F a(n) = A179119*n + O(n^(1/2)). - _Randell Heyman_, Oct 06 2022
%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]]
%t Table[Count[Table[Floor[n/k],{k,n}],_?PrimeQ],{n,80}] (* _Harvey P. Dale_, Nov 19 2022 *)
%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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