A385494 -id:A385494 - cp's OEIS frontend

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

Robert Israel, Aug 27 2025

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

			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.

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

Cf. A385494.

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);

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

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

A385494(a(n)) = n.

A387394 Total number of 2's in the decimal digits of the divisors of n.

Original entry on oeis.org

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 3, 1, 3, 1, 2, 1, 2, 1, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 3, 0, 3, 0, 2, 0, 3, 0, 2, 0, 3, 0, 2, 0, 2, 0, 2, 0, 3, 0, 2, 1, 2, 0, 3, 0, 1, 1, 1, 0, 4, 0, 1, 1, 1, 0, 2, 0, 2, 1, 2, 0, 5, 0, 1, 1, 3, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0

Offset: 1

Robert Israel, Aug 28 2025

			a(22) = 3 because among the divisors of 22, 2 has one 2 and 22 has two, for a total of 3.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A385494, A387396, A387463.

f:= proc(n) local d; add(numboccur(2, convert(d, base, 10)), d=numtheory:-divisors(n)) end proc:
map(f, [$1..200]);

a[n_]:=Count[IntegerDigits[Divisors[n]]//Flatten, 2]; Array[a, 99] (* Stefano Spezia, Aug 29 2025 *)

a(n) = sumdiv(n, d, #select(x->(x==2), digits(d))); \\ Michel Marcus, Aug 28 2025

from sympy import divisors
def a(n): return sum(str(d).count("2") for d in divisors(n, generator=True))
print([a(n) for n in range(1, 100)]) # Michael S. Branicky, Aug 29 2025

A387463 Total number of 3's in the decimal digits of the divisors of n.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 1, 1, 3, 0, 1, 2, 1, 0, 2, 1, 1, 1, 1, 0, 3, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 3, 0, 0, 2, 0, 0, 3

Offset: 1

Robert Israel, Aug 29 2025

			a(33) = 3 because among the divisors of 33, 3 has one 3 and 33 has two, for a total of 3.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A385494, A387394, A387464.

f:= proc(n) local t; add(subs(x=1, t)^3, t = expand((1+x+x^2)^n)) end proc:
map(f, [$1..100]);

a[n_]:=Count[Flatten[IntegerDigits/@Divisors[n]],3];Array[a,99] (* James C. McMahon, Aug 30 2025 *)

from sympy import divisors
def a(n): return sum(str(d).count("3") for d in divisors(n, generator=True))
print([a(n) for n in range(1, 100)]) # Michael S. Branicky, Aug 29 2025

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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.

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A387394 Total number of 2's in the decimal digits of the divisors of n.

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A387463 Total number of 3's in the decimal digits of the divisors of n.

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Maple

Mathematica

Python