|
|
A333534
|
|
a(n) is the number of log(n)-smooth numbers <= n.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,7
|
|
COMMENTS
|
Number of k <= n such that the greatest prime factor of k is <= log(n).
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
# 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)):
|
|
MATHEMATICA
|
a[n_] := Select[Range[n], FactorInteger[#][[-1, 1]] <= Log[n]&] // Length;
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|