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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.

%I A363963 #14 Apr 05 2024 13:07:07
%S A363963 1,987654103,987654301,9876541023,9876542103,9876543102,9876543201,
%T A363963 9876543210,9876542130,9876543120,9876534120,9876345120,9876514032,
%U A363963 9876431250,9876045312,9875324160,9876523104,9863147520,9875312640,9635217408,9845637120,9715064832,9574023168,9805234176,5892341760,6398410752,-1,-1,-1,536870912
%N 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.
%C A363963 a(n) = -1 for n > 29.
%e A363963 a(2) = 987654301 = 486769*2029 has distinct digits and 2 prime factors counted with multiplicity, and is the largest such number.
%p A363963 N:= 29: V:= Array(0..N,-1):
%p A363963 for m from 10 to 1 by -1 do
%p A363963   for L in combinat:-permute([9,8,7,6,5,4,3,2,1,0],m) while count < N do
%p A363963   if L[1] = 0 then break fi;
%p A363963   x:= add(L[i]*10^(m-i),i=1..m);
%p A363963   v:= numtheory:-bigomega(x);
%p A363963   if v <= N and V[v] = -1 then V[v]:= x; count:= count+1 fi
%p A363963 od od:
%p A363963 convert(V,list);
%o A363963 (Python)
%o A363963 from sympy import primeomega
%o A363963 from itertools import count, islice, permutations as P
%o A363963 def agen(): # generator of terms
%o A363963     n, adict = 0, {0:1, 1:987654103, 2:987654301} # a(1), a(2) take a while
%o A363963     D = [p for d in range(10, 0, -1) for p in P("9876543210", d) if p[0] != "0"]
%o A363963     for k in (int("".join(t)) for t in D):
%o A363963         v = primeomega(k)
%o A363963         if v not in adict:
%o A363963             adict[v] = k
%o A363963             while n in adict: yield adict[n]; n += 1
%o A363963     yield from (adict[n] if n in adict else -1 for n in count(n))
%o A363963 print(list(islice(agen(), 19))) # _Michael S. Branicky_, Apr 05 2024
%Y A363963 Cf. A029743, A320969.
%K A363963 sign,base
%O A363963 0,2
%A A363963 _Zak Seidov_ and _Robert Israel_, Jun 29 2023