A387394 -id:A387394 - cp's OEIS frontend

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

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.

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

cp's OEIS Frontend

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

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