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

1,2

Comments

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

Links

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

Formula

A385494(a(n)) = n.

Example

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.

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 *)

Prog

(Python)
from sympy import divisors
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

Crossrefs

Cf. A385494.

Sequence in context: A042413 A041212 A257313 * A335553 A122602 A037958

Adjacent sequences: A387354 A387355 A387356 * A387358 A387359 A387360

Keyword

nonn,base

Author

Robert Israel, Aug 27 2025

Status

approved