A071523 Number of 11-smooth numbers <= n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 28, 28, 28, 29, 29, 30, 30, 31, 32, 32, 32, 33, 34, 35, 35, 35, 35, 36, 37, 38, 38, 38, 38, 39, 39, 39, 40, 41, 41, 42, 42, 42, 42, 43, 43, 44

Offset

1,2

Comments

An 11-smooth number is a number of the form 2^x*3^y*5^z*7^u*11^v (x,y,z,u,v) >= 0.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = Card{ k | A051038(k) <= n }.

Mathematica

Accumulate[Table[If[Max[FactorInteger[n][[;; , 1]]]<=11, 1, 0], {n, 120}]] (* Harvey P. Dale, Sep 02 2024 *)

Prog

(PARI) a(n)=sum(k=1, n, (k<4) || 13>vecmax(factor(k)~[1, ]))
(Python)
from sympy import integer_log
def A071523(n):
    ptuple = (2, 3, 5, 7, 11)
    def g(x, m): return sum(g(x//(ptuple[m]**i), m-1)for i in range(integer_log(x, ptuple[m])[0]+1)) if m else x.bit_length()
    return g(n, 4) # Chai Wah Wu, Mar 15 2026

Crossrefs

Cf. A051038.

Number of p-smooth numbers <= n: A070939 (p=2), A071521 (p=3), A071520 (p=5), A071604 (p=7), this sequence (p=11), A080684 (p=13), A080685 (p=17), A080686 (p=19).

Sequence in context: A377293 A357030 A303219 * A297244 A070696 A053834

Adjacent sequences: A071520 A071521 A071522 * A071524 A071525 A071526

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 02 2002

Status

approved