

A068050


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


3



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, 10, 12, 14, 11, 12, 13, 14, 13, 14, 13, 14, 14, 15, 17, 18, 13, 14, 16, 17, 18, 19, 17, 19, 18, 19, 21, 22, 18, 19, 20, 21, 19, 21, 22, 23, 23, 24, 26, 27, 21, 22, 23, 24, 24, 26, 27
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OFFSET

1,5


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

If p is a prime other than 3, a(p) = a(p1) + 1.  Franklin T. AdamsWatters, Apr 27 2020


EXAMPLE

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.


MATHEMATICA

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


PROG

(Haskell)
a068050 n = length [k  k < [1..n], a010051 (n `div` k) == 1]
 Reinhard Zumkeller, Jan 31 2012


CROSSREFS

Cf. A067514.
Cf. A010051, A205745.
Sequence in context: A069360 A175509 A213023 * A210967 A343534 A275383
Adjacent sequences: A068047 A068048 A068049 * A068051 A068052 A068053


KEYWORD

easy,nonn


AUTHOR

Amarnath Murthy, Feb 12 2002


EXTENSIONS

Edited by Dean Hickerson, Feb 12 2002


STATUS

approved



