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A295084 Number of sqrt(n)-smooth numbers <= n. 9
1, 1, 1, 3, 3, 3, 3, 4, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 23, 30, 31, 31, 31, 31, 32, 32, 33, 33, 33, 33, 34, 34, 34, 35, 36, 36, 36, 36, 36, 36, 37, 37, 38, 38, 38, 39, 39, 39, 39, 39, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) = number of positive integers m<=n such that A006530(m) <= sqrt(n).

LINKS

Table of n, a(n) for n=1..80.

Wikipedia, Smooth number

FORMULA

a(n) = n - A241419(n).

If n is in A063539, then a(n)=a(n-1)+1; if n is in A001248, i.e., n=p^2 for prime p, then a(n)=a(n-1)+p; otherwise a(n)=a(n-1).

a(n) = (1 - log(2))*n + O(n/log(n)) as n -> infinity. - Robert Israel, Nov 14 2017

MAPLE

N:= 100: # to get a(1)..a(N)

G:= [0, seq(max(numtheory:-factorset(n)), n=2..N)]:

seq(nops(select(t -> t^2 <= n, G[1..n])), n=1..N); # Robert Israel, Nov 14 2017

a:=[];

for n from 1 to 100 do

   c:=0;

   for m from 1 to n do

      if A006530(m)^2 <= n then c:=c+1; fi; od:

a:=[op(a), c];

od:

a; # (Included because variants of it will apply to related sequences) - N. J. A. Sloane, Apr 10 2020

PROG

(PARI) A295084(n) = my(r=n); forprime(p=sqrtint(n)+1, n, r-=n\p); r;

CROSSREFS

Cf. A048098 (indices of records), A063539, A241419.

The following are all different versions of sqrt(n)-smooth numbers: A048098, A063539, A064775, A295084, A333535, A333536.

Sequence in context: A006671 A046074 A328914 * A068048 A176994 A264050

Adjacent sequences:  A295081 A295082 A295083 * A295085 A295086 A295087

KEYWORD

nonn,look

AUTHOR

Max Alekseyev, Nov 13 2017

STATUS

approved

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Last modified February 28 05:24 EST 2021. Contains 341695 sequences. (Running on oeis4.)