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

1, 10, 11, 60, 112, 110, 210, 330, 420, 630, 840, 1008, 1890, 1260, 1680, 2520, 2310, 3360, 5460, 6720, 4620, 5040, 7140, 7560, 11880, 9240, 14040, 10080, 17160, 13860, 17136, 16380, 15120, 18480, 27720, 33264, 21420, 39270, 30240, 36960, 41580, 45360, 42840, 57120, 60060, 71820, 75600, 55440

Offset: 1

Author

Robert Israel, Aug 27 2025

Keywords

• nonn
• base
• new

Comments

a(n) is the least number k such that A385494(k) = n.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A385494.

Programs

Maple

f:= proc(n) local t;
   add(numboccur(1, convert(t,base,10)), t = numtheory:-divisors(n))
end proc:
N:= 100: # for a(1)..a(N)
V:= Vector(N): count:= 0:
for x from 1 do
  v:= f(x);
  if v <= N and V[v] = 0 then V[v]:= x; count:= count+1; if count =  N then break fi fi;
od:
convert(V,list);

Mathematica

a[n_]:=Module[{k=1},While[Count[IntegerDigits[Divisors[k]]//Flatten,1]!=n, k++]; k]; Array[a,48] (* Stefano Spezia, Aug 28 2025 *)

Python

from itertools import count, islice
def f(n): return sum(str(d).count("1") for d in divisors(n, generator=True))
def agen(): # generator of terms
    n, adict = 1, dict()
    for k in count(1):
        v = f(k)
        if v not in adict:
            adict[v] = k
            while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 50))) # Michael S. Branicky, Aug 27 2025

Formula

A385494(a(n)) = n.