A364040 a(n) is the least positive number with distinct decimal digits and n prime factors, counted with multiplicity, or -1 if there is no such number.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 98304, 327680, 917504, 786432, 1048576, 3145728, 15728640, 31457280, 2845310976, 6398410752, -1, -1, -1, 536870912

Offset: 0

Author

Zak Seidov and Robert Israel, Jul 02 2023

Keywords

• sign
• base

Comments

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

Examples

			a(5) = 32 = 2^5 has distinct decimal digits and 5 prime factors counted with multiplicity.
		

Crossrefs

Cf. A363963.

Programs

Maple

V:= Array(0..29,-1): count:= 0:
for m from 1 to 10 do
  for L in combinat:-permute([$0..9],m) while count < 27 do
    if L[1] = 0 then next fi;
    x:= add(L[i]*10^(m-i),i=1..m);
    v:= numtheory:-bigomega(x);
    if 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
    adict, n = dict(), 0
    D = [p for d in range(1, 11) for p in P("0123456789", 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(), 22))) # Michael S. Branicky, Apr 05 2024