A108276 Number of positive integers <= 10^n that are divisible by no prime exceeding 19.

1, 10, 72, 331, 1169, 3419, 8751, 20198, 42950, 85411, 160626, 288126, 496303, 825326, 1330766, 2088013, 3197529, 4791093, 7039193, 10159603, 14427309, 20186026, 27861175, 37974797, 51162295, 68191379, 89983125, 117635672

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..150

Mathematica

n = 9; t = 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 &]; Table[ Length[ Select[t, # <= 10^n &]], {n, 0, 10}]

Prog

(Python)
from sympy import integer_log
def A108276(n):
    ptuple = (2, 3, 5, 7, 11, 13, 17, 19)
    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, 7) # Chai Wah Wu, Mar 16 2026

Crossrefs

Row 8 of A253635.

Cf. A123384, A100752, A106598, A106600, A107352, A106629, A108275, A108277, A011557, A080682.

Sequence in context: A037579 A166791 A271035 * A264159 A228316 A228310

Adjacent sequences: A108273 A108274 A108275 * A108277 A108278 A108279

Keyword

nonn

Author

Robert G. Wilson v, May 31 2005

Extensions

a(10)-a(18) from Donovan Johnson, Sep 16 2009

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

Status

approved