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A295101 Number of squarefree sqrt(n)-smooth numbers <= n. 3

%I

%S 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,

%T 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,

%U 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

%N Number of squarefree sqrt(n)-smooth numbers <= n.

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

%H Robert Israel, <a href="/A295101/b295101.txt">Table of n, a(n) for n = 1..10000</a>

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

%F 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).

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

%p V:= Vector(N,1):

%p for n from 2 to N do

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

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

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

%p od:

%p convert(V,list); # _Robert Israel_, Mar 24 2020

%Y Cf. A005117, A013928, A295084.

%K nonn,look

%O 1,4

%A _Max Alekseyev_, Nov 14 2017

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Last modified July 26 10:35 EDT 2021. Contains 346294 sequences. (Running on oeis4.)