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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.

%I A364040 #12 Apr 05 2024 13:02:21
%S A364040 1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,98304,
%T A364040 327680,917504,786432,1048576,3145728,15728640,31457280,2845310976,
%U A364040 6398410752,-1,-1,-1,536870912
%N 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.
%C A364040 a(n) = -1 for n > 29.
%e A364040 a(5) = 32 = 2^5 has distinct decimal digits and 5 prime factors counted with multiplicity.
%p A364040 V:= Array(0..29,-1): count:= 0:
%p A364040 for m from 1 to 10 do
%p A364040   for L in combinat:-permute([$0..9],m) while count < 27 do
%p A364040     if L[1] = 0 then next fi;
%p A364040     x:= add(L[i]*10^(m-i),i=1..m);
%p A364040     v:= numtheory:-bigomega(x);
%p A364040     if V[v] = -1 then V[v]:= x; count:= count+1 fi;
%p A364040   od;
%p A364040 od:
%p A364040 convert(V,list);
%o A364040 (Python)
%o A364040 from sympy import primeomega
%o A364040 from itertools import count, islice, permutations as P
%o A364040 def agen(): # generator of terms
%o A364040     adict, n = dict(), 0
%o A364040     D = [p for d in range(1, 11) for p in P("0123456789", d) if p[0] != "0"]
%o A364040     for k in (int("".join(t)) for t in D):
%o A364040         v = primeomega(k)
%o A364040         if v not in adict:
%o A364040             adict[v] = k
%o A364040             while n in adict: yield adict[n]; n += 1
%o A364040     yield from (adict[n] if n in adict else -1 for n in count(n))
%o A364040 print(list(islice(agen(), 22))) # _Michael S. Branicky_, Apr 05 2024
%Y A364040 Cf. A363963.
%K A364040 sign,base
%O A364040 0,2
%A A364040 _Zak Seidov_ and _Robert Israel_, Jul 02 2023