A083903 Number of divisors of n with largest digit <= 8 (base 10).

1, 2, 2, 3, 2, 4, 2, 4, 2, 4, 2, 6, 2, 4, 4, 5, 2, 5, 1, 6, 4, 4, 2, 8, 3, 4, 3, 6, 1, 8, 2, 6, 4, 4, 4, 8, 2, 3, 3, 8, 2, 8, 2, 6, 5, 4, 2, 10, 2, 6, 4, 6, 2, 7, 4, 8, 3, 3, 1, 12, 2, 4, 5, 7, 4, 8, 2, 6, 3, 8, 2, 11, 2, 4, 6, 5, 4, 7, 1, 10, 4, 4, 2, 12, 4, 4, 3, 8, 1, 10, 3, 5, 3, 3, 2, 11, 1, 4, 4, 9, 2, 8

Offset: 1

Author

Reinhard Zumkeller, May 08 2003

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A054055, A000005, A007095, A082838, A083895, A083896, A083902.

Programs

Mathematica

Table[Length[DeleteCases[Divisors[n],?(Max[IntegerDigits[#]]==9&)]],{n,110}] (* _Harvey P. Dale, Nov 21 2015 *)

Formula

a(n) = A083902(n) + A083895(n) = A000005(n) - A083896(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A007095(k) = 22.920676... (A082838). - Amiram Eldar, Jan 04 2024