A083902 Number of divisors of n with the largest digit of the divisor <= 7 (base 10).

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

Offset: 1

Author

Reinhard Zumkeller, May 08 2003

Keywords

• nonn
• base

Crossrefs

Cf. A054055, A000005, A007094, A083894, A083895, A083901, A083903.

Programs

Mathematica

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]<8&)],{n,110}] (* _Harvey P. Dale, Nov 01 2022 *)

Formula

a(n) = A083901(n) + A083894(n) = A083903(n) - A083895(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A007094(k) = 11.2915816168324913817... . - Amiram Eldar, Jan 04 2024

Extensions

Definition clarified by Harvey P. Dale, Nov 01 2022