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A387357 a(n) is the first number with a total of exactly n 1's in the decimal digits of its divisors.

%I A387357 #14 Aug 29 2025 10:16:30
%S A387357 1,10,11,60,112,110,210,330,420,630,840,1008,1890,1260,1680,2520,2310,
%T A387357 3360,5460,6720,4620,5040,7140,7560,11880,9240,14040,10080,17160,
%U A387357 13860,17136,16380,15120,18480,27720,33264,21420,39270,30240,36960,41580,45360,42840,57120,60060,71820,75600,55440
%N A387357 a(n) is the first number with a total of exactly n 1's in the decimal digits of its divisors.
%C A387357 a(n) is the least number k such that A385494(k) = n.
%H A387357 Robert Israel, <a href="/A387357/b387357.txt">Table of n, a(n) for n = 1..400</a>
%F A387357 A385494(a(n)) = n.
%e A387357 a(6) = 110 because of the divisors of 110, 1 and 10 each have one 1, 11 and 110 each have two, for a total of 6, and no smaller number works.
%p A387357 f:= proc(n) local t;
%p A387357    add(numboccur(1, convert(t,base,10)), t = numtheory:-divisors(n))
%p A387357 end proc:
%p A387357 N:= 100: # for a(1)..a(N)
%p A387357 V:= Vector(N): count:= 0:
%p A387357 for x from 1 do
%p A387357   v:= f(x);
%p A387357   if v <= N and V[v] = 0 then V[v]:= x; count:= count+1; if count =  N then break fi fi;
%p A387357 od:
%p A387357 convert(V,list);
%t A387357 a[n_]:=Module[{k=1},While[Count[IntegerDigits[Divisors[k]]//Flatten,1]!=n, k++]; k]; Array[a,48] (* _Stefano Spezia_, Aug 28 2025 *)
%o A387357 (Python)
%o A387357 from itertools import count, islice
%o A387357 def f(n): return sum(str(d).count("1") for d in divisors(n, generator=True))
%o A387357 def agen(): # generator of terms
%o A387357     n, adict = 1, dict()
%o A387357     for k in count(1):
%o A387357         v = f(k)
%o A387357         if v not in adict:
%o A387357             adict[v] = k
%o A387357             while n in adict: yield adict[n]; n += 1
%o A387357 print(list(islice(agen(), 50))) # _Michael S. Branicky_, Aug 27 2025
%Y A387357 Cf. A385494.
%K A387357 nonn,base,new
%O A387357 1,2
%A A387357 _Robert Israel_, Aug 27 2025