A363963 a(n) is the greatest number with distinct decimal digits and n prime factors, counted with multiplicity, or -1 if there is no such number.

1, 987654103, 987654301, 9876541023, 9876542103, 9876543102, 9876543201, 9876543210, 9876542130, 9876543120, 9876534120, 9876345120, 9876514032, 9876431250, 9876045312, 9875324160, 9876523104, 9863147520, 9875312640, 9635217408, 9845637120, 9715064832, 9574023168, 9805234176, 5892341760, 6398410752, -1, -1, -1, 536870912

Offset: 0

Author

Zak Seidov and Robert Israel, Jun 29 2023

Keywords

• sign
• base

Comments

a(n) = -1 for n > 29.

Examples

			a(2) = 987654301 = 486769*2029 has distinct digits and 2 prime factors counted with multiplicity, and is the largest such number.
		

Crossrefs

Cf. A029743, A320969.

Programs

Maple

N:= 29: V:= Array(0..N,-1):
for m from 10 to 1 by -1 do
  for L in combinat:-permute([9,8,7,6,5,4,3,2,1,0],m) while count < N do
  if L[1] = 0 then break fi;
  x:= add(L[i]*10^(m-i),i=1..m);
  v:= numtheory:-bigomega(x);
  if v <= N and V[v] = -1 then V[v]:= x; count:= count+1 fi
od od:
convert(V,list);

Python

from sympy import primeomega
from itertools import count, islice, permutations as P
def agen(): # generator of terms
    n, adict = 0, {0:1, 1:987654103, 2:987654301} # a(1), a(2) take a while
    D = [p for d in range(10, 0, -1) for p in P("9876543210", d) if p[0] != "0"]
    for k in (int("".join(t)) for t in D):
        v = primeomega(k)
        if v not in adict:
            adict[v] = k
            while n in adict: yield adict[n]; n += 1
    yield from (adict[n] if n in adict else -1 for n in count(n))
print(list(islice(agen(), 19))) # Michael S. Branicky, Apr 05 2024