

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(n1)+1; if n is in A001248, i.e., n=p^2 for prime p, then a(n)=a(n1)+A013928(p); otherwise a(n)=a(n1).


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



