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

Author

Robert Israel, Aug 28 2025

Keywords

• nonn
• base
• new

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A387357, A387394, A387464.

Programs

Maple

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);

Mathematica

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

PARI

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

Python

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

Formula

A387394(a(n)) = n.