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

1,40

Links

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

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

Example

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

Mathematica

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

Prog

(PARI) a(n) = my(x = n%10); sumdiv(n, d, if (d<n, d%10 == x)); \\ Michel 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

Crossrefs

Cf. A010879, A032741, A330348.

Sequence in context: A114640 A056890 A321519 * A169590 A300185 A262804

Adjacent sequences: A346389 A346390 A346391 * A346393 A346394 A346395

Keyword

nonn,base

Author

Stefano Spezia, Jul 15 2021

Status

approved