A387463 Total number of 3's in the decimal digits of the divisors of n.

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

Author

Robert Israel, Aug 29 2025

Keywords

• nonn
• new

Examples

			a(33) = 3 because among the divisors of 33, 3 has one 3 and 33 has two, for a total of 3.
		

Links

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

Crossrefs

Cf. A385494, A387394, A387464.

Programs

Maple

f:= proc(n) local t; add(subs(x=1, t)^3, t = expand((1+x+x^2)^n)) end proc:
map(f, [$1..100]);

Mathematica

a[n_]:=Count[Flatten[IntegerDigits/@Divisors[n]],3];Array[a,99] (* James C. McMahon, Aug 30 2025 *)

Python

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