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

0,2

Comments

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

Links

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

Formula

A387394(a(n)) = n.

Example

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.

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 *)

Prog

(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 sympy import divisors
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

Crossrefs

Cf. A387357, A387394, A387464.

Sequence in context: A244188 A189330 A120672 * A190642 A108960 A111095

Adjacent sequences: A387393 A387394 A387395 * A387397 A387398 A387399

Keyword

nonn,base

Author

Robert Israel, Aug 28 2025

Status

approved