A083892 Number of divisors of n with largest digit = 5 (base 10).

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 1, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 1, 0, 1, 4

Offset: 1

Author

Reinhard Zumkeller, May 08 2003

Keywords

• nonn
• base

Examples

			n=125, 3 of the 4 divisors of 125 have largest digit =5: {5,25,125}, therefore a(125)=3.
		

Links

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

Crossrefs

Cf. A054055, A000005, A083900, A083888, A083889, A083890, A083891, A083893, A083894, A083895, A083896, A283608.

Programs

Maple

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 5:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Mathematica

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]==5&)],{n,110}] (* _Harvey P. Dale, Aug 08 2015 *)

Formula

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083900(n) - A083899(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283608(k) = 1.32926350368137107677... . - Amiram Eldar, Jan 04 2024