A083899 Number of divisors of n with largest digit <= 4 (base 10).

1, 2, 2, 3, 1, 3, 1, 3, 2, 3, 2, 5, 2, 3, 2, 3, 1, 3, 1, 5, 3, 4, 2, 6, 1, 3, 2, 4, 1, 5, 2, 4, 4, 3, 1, 5, 1, 2, 3, 6, 2, 6, 2, 6, 2, 3, 1, 6, 1, 3, 2, 4, 1, 3, 2, 4, 2, 2, 1, 8, 1, 3, 3, 4, 2, 6, 1, 4, 3, 4, 1, 6, 1, 2, 2, 3, 2, 4, 1, 6, 2, 3, 1, 8, 1, 3, 2, 6, 1, 5, 2, 4, 3, 2, 1, 7, 1, 3, 4, 6, 2, 5, 2, 5, 3

Offset: 1

Author

Reinhard Zumkeller, May 08 2003

Keywords

• nonn
• base

Crossrefs

Cf. A054055, A000005, A007091, A083891, A083892, A083898, A083900.

Programs

Mathematica

a[n_] := DivisorSum[n, 1 &, Max[IntegerDigits[#]] <= 4 &]; Array[a, 100] (* Amiram Eldar, Jan 04 2024 *)

Formula

a(n) = A083898(n) + A083891(n) = A083900(n) - A083892(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A007091(k) = 3.92521682598923397031... . - Amiram Eldar, Jan 04 2024