A083903 - OEIS

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

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OFFSET

1,2

LINKS

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

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

MATHEMATICA

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

CROSSREFS

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