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

Author

Benoit Cloitre, Jun 02 2002

Keywords

• easy
• nonn

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

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).

Programs

Mathematica

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

PARI

a(n)=sum(k=1,n,(k<4) || 13>vecmax(factor(k)~[1,]))

Formula

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