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

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

Author

Robert Israel, Aug 28 2025

Keywords

• nonn
• base
• new

Examples

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

Links

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

Crossrefs

Cf. A385494, A387396, A387463.

Programs

Maple

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

Mathematica

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

PARI

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

Python

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