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
Examples
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
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
Programs
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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 *) -
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
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Python
# see linked program
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