A333534 a(n) is the number of log(n)-smooth numbers <= n.
0, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19
Offset: 2
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 2..65536
Programs
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Maple
A333534 := n -> nops(select(k -> A006530(k) <= ilog(n), [$1..n])): seq(A333534(n), n=2..86); # Peter Luschny, Apr 09 2020 # second Maple program: b:= proc(n) option remember; max(1, map(i-> i[1], ifactors(n)[2])) end: a:= n-> (t-> add(`if`(b(i)<= t, 1, 0), i=1..n))(ilog(n)): seq(a(n), n=2..100); # Alois P. Heinz, Apr 09 2020
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Mathematica
a[n_] := Select[Range[n], FactorInteger[#][[-1, 1]] <= Log[n]&] // Length; a /@ Range[2, 100] (* Jean-François Alcover, May 17 2020 *)
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PARI
gpf(j)={if(j==1,1,my(f=factor(j));f[#f[,2],1])}; for(n=2,80,my(L=log(n));print1(sum(k=1,n,gpf(k)<=L),", ")) \\ Hugo Pfoertner, Apr 09 2020 -
PARI
sm(lim, p)=if(p==2, return(logint(lim\1, 2)+1)); my(s=0, q=precprime(p-1), t=1); for(e=0, logint(lim\=1, p), s+=sm(lim\t, q); t*=p); s a(n)=if(n<8,return(n>2)); sm(n, precprime(log(n))) \\ Charles R Greathouse IV, Apr 16 2020
Formula
a(n) = A096300(n), n>2. - R. J. Mathar, Apr 27 2020
Comments