A387357 -id:A387357 - cp's OEIS frontend

A385494 Total number of 1's in the decimal digits of the divisors of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 2, 1, 3, 2, 2, 3, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 3, 2, 1, 1, 3, 1, 2, 3, 2, 1, 2, 3, 2, 2, 1, 1, 4, 2, 2, 2, 2, 2, 3, 1, 2, 1, 3, 2, 3, 1, 1, 2, 2, 3, 2, 1, 3, 2, 2, 1, 4, 2, 1, 1, 3, 1, 4, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3

Offset: 1

Robert Israel, Aug 27 2025

			a(11) = 3 because of the divisors of 11, there is one 1 in 1 and two in 11.
a(60) = 4 because of the divisors of 60, there is one 1 in 1, one in 10, one in 12, one in 15 and none in the other divisors.

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

Cf. A093653, A387357.

f:= proc(n) local d; add(numboccur(1, convert(d,base,10)),d=numtheory:-divisors(n)) end proc:
map(f, [$1..100]);

a[n_]:=Count[IntegerDigits[Divisors[n]]//Flatten,1]; Array[a,100] (* Stefano Spezia, Aug 28 2025 *)

a(n) = sumdiv(n, d, #select(x->(x==1), digits(d))); \\ Michel Marcus, Aug 28 2025

from sympy import divisors
def a(n): return sum(str(d).count("1") for d in divisors(n, generator=True))
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Aug 27 2025

A387396 a(n) is the smallest positive number with a total of exactly n 2's in the decimal digits of its divisors.

Original entry on oeis.org

1, 2, 12, 22, 72, 84, 168, 264, 252, 756, 504, 672, 1260, 1512, 2184, 2640, 2772, 2016, 2520, 4032, 5544, 5040, 6048, 6720, 7392, 13104, 12096, 16632, 10080, 15120, 18144, 21840, 33600, 25200, 34320, 22176, 20160, 34272, 30240, 42840, 45360, 36960, 50400, 52416, 55440, 94248, 65520, 66528, 60480

Offset: 0

Robert Israel, Aug 28 2025

a(n) is the least number k such that A387394(k) = n.

			a(3) = 22 because of the divisors of 22, 2 has one 2, 22 has two, for a total of 3, and 22 is the smallest number that works.

Robert Israel, Table of n, a(n) for n = 0..371

Cf. A387357, A387394, A387464.

ff:= proc(n) option remember; numboccur(2, convert(n, base, 10)) end proc:
f:= proc(n) local d; add(ff(d), d=numtheory:-divisors(n)) end proc:
V:= Array(0..50): count:= 0:
for x from 1 while count < 51 do
  v:= f(x); if v <= 50 and V[v] = 0 then V[v]:= x; count:= count+1; fi
od:
convert(V,list);

a[n_]:=Module[{k=1}, While[Count[IntegerDigits[Divisors[k]]//Flatten, 2]!=n, k++]; k]; Array[a, 49,0] (* Stefano Spezia, Aug 29 2025 *)

f(n) = sumdiv(n, d, #select(x->(x==2), digits(d))); \\ A387394
a(n) = my(k=1); while(f(k) !=n, k++); k; \\ Michel Marcus, Aug 28 2025

from itertools import count, islice
def f(n): return sum(str(d).count("2") for d in divisors(n, generator=True))
def agen(): # generator of terms
    n, adict = 0, 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 29 2025

A387394(a(n)) = n.

cp's OEIS Frontend

A385494 Total number of 1's in the decimal digits of the divisors of n.

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