A108277 Number of positive integers <= 10^n that are divisible by no prime exceeding 23.

1, 10, 76, 369, 1385, 4298, 11654, 28434, 63768, 133440, 263529, 495412, 892644, 1550012, 2605342, 4254753, 6771752, 10531080, 16038303, 23965659, 35195450, 50872227, 72464493, 101837746, 141340075, 193902062, 263152095, 353549942

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..111

Mathematica

n = 6; t = Select[ Flatten[ Table[23^i*Select[ Flatten[ Table[19^h*Select[ Flatten[ Table[17^g*Select[ Flatten[ Table[13^f*Select[ Flatten[ Table[11^e*Select[ Flatten[ Table[7^d*Select[ Flatten[ Table[5^c*Select[ Flatten[ Table[2^a*3^b, {a, 0, n*Log[2, 10]}, {b, 0, n*Log[3, 10]}]], # <= 10^n &], {c, 0, n*Log[5, 10]}]], # <= 10^n &], {d, 0, n*Log[7, 10]}]], # <= 10^n &], {e, 0, n*Log[11, 10]}]], # <= 10^n &], {f, 0, n*Log[13, 10]}]], # <= 10^n &], {g, 0, n*Log[17, 10]}]], # <= 10^n &], {h, 0, n*Log[19, 10]}]], # <= 10^n &], {i, 0, n*Log[23, 10]}]], # <= 10^n &]; Table[ Length[ Select[t, # <= 10^n &]], {n, 0, 10}]

Prog

(Python)
from sympy import integer_log
def A108277(n):
    ptuple = (2, 3, 5, 7, 11, 13, 17, 19, 23)
    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(10**n, 8) # Chai Wah Wu, Mar 16 2026

Crossrefs

Row 9 of A253635.

Cf. A123384, A100752, A106598, A106600, A107352, A106629, A108275, A108276, A011557, A080683.

Sequence in context: A049392 A136869 A368418 * A061319 A223994 A016149

Adjacent sequences: A108274 A108275 A108276 * A108278 A108279 A108280

Keyword

nonn

Author

Robert G. Wilson v, May 31 2005

Extensions

a(7)-a(18) from Donovan Johnson, Sep 16 2009

a(19)-a(27) from Max Alekseyev, Apr 28 2010

Status

approved