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A355771 a(n) is the smallest integer that has exactly n divisors from A333369.

%I A355771 #36 Jul 30 2022 12:53:26
%S A355771 1,3,9,15,45,105,195,315,945,900,1575,2100,3900,6825,11655,10500,6300,
%T A355771 18900,25200,35100,27300,31500,44100,94500,157500,107100,81900,233100,
%U A355771 220500,598500,245700,333900,409500,491400,900900,573300,600600,1228500,1669500,1965600
%N A355771 a(n) is the smallest integer that has exactly n divisors from A333369.
%H A355771 Michael S. Branicky, <a href="/A355771/b355771.txt">Table of n, a(n) for n = 1..87</a>
%e A355771 15 has 4 divisors: {1, 3, 5, 15} all of which are in A333369 integers, and no smaller number has this property, hence a(4) = 15.
%t A355771 q[n_] := AllTrue[Tally @ IntegerDigits[n], EvenQ[Plus @@ #] &]; f[n_] := DivisorSum[n, 1 &, q[#] &]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n]; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[40, 10^7] (* _Amiram Eldar_, Jul 17 2022 *)
%o A355771 (PARI) issimber(m) = my(d=digits(m), s=Set(d)); for (i=1, #s, if (#select(x->(x==s[i]), d) % 2 != (s[i] % 2), return (0))); return (1); \\ A333369
%o A355771 a(n) = my(k=1); while (sumdiv(k, d, issimber(d)) != n, k++); k; \\ _Michel Marcus_, Jul 18 2022
%o A355771 (Python)
%o A355771 from sympy import divisors
%o A355771 from itertools import count, islice
%o A355771 def c(n): s = str(n); return all(s.count(d)%2 == int(d)%2 for d in set(s))
%o A355771 def f(n): return sum(1 for d in divisors(n, generator=True) if c(d))
%o A355771 def agen():
%o A355771     n, adict = 1, dict()
%o A355771     for k in count(1):
%o A355771         fk = f(k)
%o A355771         if fk not in adict: adict[fk] = k
%o A355771         while n in adict: yield adict[n]; n += 1
%o A355771 print(list(islice(agen(), 29))) # _Michael S. Branicky_, Jul 23 2022
%Y A355771 Cf. A333369, A353735, A355770, A355772, A355773.
%Y A355771 Cf. A005231, A053624.
%Y A355771 Similar sequences: A087997, A333456, A355303, A355699.
%K A355771 nonn,base
%O A355771 1,2
%A A355771 _Bernard Schott_, Jul 17 2022
%E A355771 More terms from _Amiram Eldar_, Jul 17 2022