A346392 - OEIS

%I #30 Jul 31 2021 19:50:42

%S 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,

%T 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,

%U 0,1,1,2,0,0,3,0,1,0,0,3,1,1,0,2,1,0,0,1,0,2

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

%H Michael S. Branicky, <a href="/A346392/b346392.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A330348(n) - 1. - _Michel Marcus_, Jul 19 2021

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

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

%o (PARI) a(n) = my(x = n%10); sumdiv(n, d, if (d<n, d%10 == x)); \\ _Michel Marcus_, Jul 19 2021

%o (Python)

%o from sympy import divisors

%o def a(n): return sum(d%10 == n%10 for d in divisors(n)[:-1])

%o print([a(n) for n in range(1, 91)]) # _Michael S. Branicky_, Jul 31 2021

%Y Cf. A010879, A032741, A330348.

%K nonn,base

%O 1,40

%A _Stefano Spezia_, Jul 15 2021