A346392 a(n) is the number of proper divisors of n ending with the same digit as n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 3, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 3, 0, 1, 0, 0, 3, 1, 1, 0, 2, 1, 0, 0, 1, 0, 2

Offset: 1

Author

Stefano Spezia, Jul 15 2021

Keywords

• nonn
• base

Examples

			a(40) = 2 since there are 2 proper divisors of 40 ending with 0: 10 and 20.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010879, A032741, A330348.

Programs

Mathematica

a[n_]:=Length[Drop[Select[Divisors[n], (Mod[#,10]==Mod[n,10]&)], -1]]; Array[a, 90]

PARI

a(n) = my(x = n%10); sumdiv(n, d, if (dMichel Marcus, Jul 19 2021

Python

from sympy import divisors
def a(n): return sum(d%10 == n%10 for d in divisors(n)[:-1])
print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Jul 31 2021

Formula

For a prime p, a(p) = 1 if p has the final digit equal to 1, otherwise a(p) = 0.

a(n) = A330348(n) - 1. - Michel Marcus, Jul 19 2021