A083896 Number of divisors of n with largest digit = 9 (base 10).

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

Offset: 1

Author

Reinhard Zumkeller, May 08 2003

Keywords

• nonn
• base

Examples

			n = 117, 2 of the 6 divisors of 117 have largest digit = 9: {9,39}, therefore a(117) = 2.
		

Links

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

Crossrefs

Cf. A054055, A000005, A083888, A083889, A083890, A083891, A083892, A083893, A083894, A083895.

Cf. A001620, A082838.

Programs

Maple

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 9:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Mathematica

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]==9&)],{n,110}] (* _Harvey P. Dale, Mar 15 2018 *)

Formula

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) = A000005(n) - A083903(n).

Sum_{k=1..n} a(k) ~ n * (log(n) + c), where c = 2*A001620 - 1 - A082838 = -22.766245... . - Amiram Eldar, Apr 17 2025