OFFSET
1,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Randell Heyman, Cardinality of a floor function, arXiv:1905.00533 [math.NT], 2019.
Randell Heyman, Primes in floor function sets, arXiv:2111.00408 [math.NT], 2021
Randell Heyman, Primes in floor function sets, INTEGERS, vol. 22, 2022, A59.
FORMULA
a(n) = 4*n^(1/2)/log(n) + O(n^(1/2)/(log(n))^2). - Randell Heyman, Oct 06 2022
EXAMPLE
a(10)=3 as floor(10/k) for k = 1 to 10 is 10,5,3,2,2,1,1,1,1,1, respectively; the 3 primes are 5,3,2.
MATHEMATICA
a[n_] := Length[Union[Select[Table[Floor[n/i], {i, 1, n}], PrimeQ]]]
Table[PrimeNu[Product[Floor[n/k], {k, 1, n}]], {n, 1, 100}] (* G. C. Greubel, May 08 2017 *)
PROG
(PARI) a(n) = #select(x->isprime(x), Set(vector(n, k, n\k))); \\ Michel Marcus, May 04 2019
(PARI) a(n)=my(s=sqrtint(n+1)); sum(k=1, s, isprime(n\k))+primepi(n\s-1) \\ Charles R Greathouse IV, Nov 05 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Feb 12 2002
EXTENSIONS
Edited by Dean Hickerson, Feb 12 2002
STATUS
approved