A074112
Let omega(m) be the number of distinct prime divisors of m. Then a(n) is the largest n-digit squarefree number such that omega(n) > omega(j) for all j < n.
Original entry on oeis.org
6, 78, 966, 9870, 99330, 930930, 9699690, 99953490, 999068070, 9592993410, 99978788910, 999890501610, 9814524629910, 99999887777790, 998448347106210, 9999999768941490, 99992911041433410, 997799870344687410, 9999839051940347610, 99987077573596883670
Offset: 1
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A074112 := proc(n)
option remember;
local a,o,wrks,j ;
if n = 1 then
return 6;
end if;
for a from 10^n-1 to 10^(n-2) by -1 do
if numtheory[issqrfree](a) then
o := omega(a) ;
wrks := true;
for j from 1 to n-1 do
if omega(procname(j)) >= o then
wrks := false;
break;
end if;
end do:
if wrks then
return a;
end if;
end if;
end do:
return -1 ;
end proc:
for j from 1 do
print( A074112(j)) ;
end do: # R. J. Mathar, Oct 03 2014
A091800
Largest n-digit number with maximal number of distinct prime divisors.
Original entry on oeis.org
6, 90, 990, 9870, 99330, 930930, 9699690, 99981420, 999068070, 9592993410, 99978788910, 999890501610, 9814524629910, 99999887777790, 999192361827660, 9999999768941490, 99992911041433410, 997799870344687410, 9999847102571786460, 99987077573596883670, 999999011467253427630, 9999928946485603635510
Offset: 1
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
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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 *)
-
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
-
# see linked program
A231209
Smallest squarefree number k with 2^n ways to write k as k = x*y, where x, y = squarefree numbers, 1 <= x <= y <= k.
Original entry on oeis.org
1, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070
Offset: 0
a(0)=1 because squarefree number k=1 with 2^0=1 way to write k = x*y = 1*1 where x=1 and y=1 are squarefree numbers;
a(1)=6 because squarefree number k=6 with 2^1=2 ways to write k = x*y = 1*6 = 2*3 where 1, 6, 2, 3, are all squarefree numbers;
a(2)=30 because squarefree number k=30 with 2^2=4 ways to write k = 1*30 = 2*15 = 3*10 = 5*6 where 1, 30, 2, 15, 3, 10, 5, 6 are all squarefree numbers;
a(3)=210 because squarefree number k=210 with 2^3=8 ways to write k = 1*210 = 2*105 = 3*70 = 5*42 = 6*35 = 7*30 = 10*21 = 14*15 where 1, 210, 2, 105, 3, 70, 5, 42, 6, 35, 7, 30, 10, 21, 14, 15 are all squarefree numbers.
Showing 1-3 of 3 results.
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