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A295101 Number of squarefree sqrt(n)-smooth numbers <= n. 3
1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A013928(n+1) - Sum_{prime p > sqrt(n)} A013928(floor(n/p)+1).

If n is in A295102, 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)+A013928(p); otherwise a(n)=a(n-1).

MAPLE

N:= 200: # for a(1)..a(N)

V:= Vector(N, 1):

for n from 2 to N do

   if not numtheory:-issqrfree(n) then next fi;

   m:= max(max(numtheory:-factorset(n))^2, n);

   if m <= N then V[m..N]:= map(`+`, V[m..N], 1) fi;

od:

convert(V, list); # Robert Israel, Mar 24 2020

CROSSREFS

Cf. A005117, A013928, A295084.

Sequence in context: A319799 A294078 A064133 * A160675 A105674 A130496

Adjacent sequences:  A295098 A295099 A295100 * A295102 A295103 A295104

KEYWORD

nonn,look

AUTHOR

Max Alekseyev, Nov 14 2017

STATUS

approved

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Last modified June 16 16:55 EDT 2021. Contains 345064 sequences. (Running on oeis4.)