cp's OEIS Frontend

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

%I A091800 #38 Aug 22 2025 17:54:24
%S A091800 6,90,990,9870,99330,930930,9699690,99981420,999068070,9592993410,
%T A091800 99978788910,999890501610,9814524629910,99999887777790,
%U A091800 999192361827660,9999999768941490,99992911041433410,997799870344687410,9999847102571786460,99987077573596883670,999999011467253427630,9999928946485603635510
%N A091800 Largest n-digit number with maximal number of distinct prime divisors.
%H A091800 Michael S. Branicky, <a href="/A091800/b091800.txt">Table of n, a(n) for n = 1..54</a> (terms 1..28 from John Reimer Morales and David A. Corneth)
%H A091800 Michael S. Branicky, <a href="/A091800/a091800.py.txt">Python program for OEIS A091800</a>
%e A091800 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
%t A091800 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 *)
%o A091800 (Python)
%o A091800 from sympy import nextprime, factorint
%o A091800 def A091800(n: int) -> int:
%o A091800     k, p, r, t = 0, 1, 1, 10**n
%o A091800     while r < t:
%o A091800        p = nextprime(p)
%o A091800        r *= p
%o A091800        k += 1
%o A091800     m = t - 1
%o A091800     while len(factorint(m)) != k - 1: m -= 1
%o A091800     return m # _John Reimer Morales_, Aug 18 2025
%o A091800 (Python) # see linked program
%Y A091800 Cf. A000005, A002182, A002183, A066151, A074111.
%K A091800 nonn,base,changed
%O A091800 1,1
%A A091800 _Amarnath Murthy_, Feb 21 2004
%E A091800 Edited, corrected and extended by _Ray Chandler_, Feb 23 2004
%E A091800 a(10)-a(12) from _Amiram Eldar_, Mar 03 2020
%E A091800 a(13) from _Giovanni Resta_, Mar 04 2020
%E A091800 a(14) onwards from _John Reimer Morales_ and _David A. Corneth_, Aug 19 2025