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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

Alois P. Heinz, Table of n, a(n) for n = 2..65536

FORMULA

a(n) = A096300(n), n>2. - R. J. Mathar, Apr 27 2020

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

MATHEMATICA

a[n_] := Select[Range[n], FactorInteger[#][[-1, 1]] <= Log[n]&] // Length;

a /@ Range[2, 100] (* Jean-Fran├žois Alcover, May 17 2020 *)

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

a(n)=if(n<8, return(n>2)); sm(n, precprime(log(n))) \\ Charles R Greathouse IV, Apr 16 2020

CROSSREFS

Cf. A001671, A006530, A051102, A137845, A295084.

Sequence in context: A066014 A080678 A096300 * A035672 A113472 A105682

Adjacent sequences:  A333531 A333532 A333533 * A333535 A333536 A333537

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 08 2020

STATUS

approved

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Last modified August 7 11:46 EDT 2020. Contains 336276 sequences. (Running on oeis4.)