A091800 Largest n-digit number with maximal number of distinct prime divisors.

6, 90, 990, 9870, 99330, 930930, 9699690, 99981420, 999068070, 9592993410, 99978788910, 999890501610, 9814524629910, 99999887777790, 999192361827660, 9999999768941490, 99992911041433410, 997799870344687410, 9999847102571786460, 99987077573596883670, 999999011467253427630, 9999928946485603635510

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..54 (terms 1..28 from John Reimer Morales and David A. Corneth)

Michael S. Branicky, Python program for OEIS A091800

Example

a(4) = 9870 as the largest number of distinct prime factors any 4-digit number can have and any number 9871 <= k <= 9999 has fewer than 5 prime factors. - David A. Corneth, Aug 19 2025

Mathematica

a[n_] := Module[{k=0, p=1, r=1, t=10^n}, While[r < t, p = NextPrime[p]; r *= p; k++]; k--; m = t-1; While[PrimeNu[m] != k, m--]; m]; Array[a, 8] (* Amiram Eldar, Mar 03 2020 *)

Prog

(Python)
from sympy import nextprime, factorint
def A091800(n: int) -> int:
    k, p, r, t = 0, 1, 1, 10**n
    while r < t:
       p = nextprime(p)
       r *= p
       k += 1
    m = t - 1
    while len(factorint(m)) != k - 1: m -= 1
    return m # John Reimer Morales, Aug 18 2025
(Python) # see linked program

Crossrefs

Cf. A000005, A002182, A002183, A066151, A074111.

Sequence in context: A177283 A121607 A100594 * A336042 A353230 A317487

Adjacent sequences: A091797 A091798 A091799 * A091801 A091802 A091803

Keyword

nonn,base

Author

Amarnath Murthy, Feb 21 2004

Extensions

Edited, corrected and extended by Ray Chandler, Feb 23 2004

a(10)-a(12) from Amiram Eldar, Mar 03 2020

a(13) from Giovanni Resta, Mar 04 2020

a(14) onwards from John Reimer Morales and David A. Corneth, Aug 19 2025

Status

approved