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Number of divisors of n with largest digit <= 6 (base 10).
4

%I #8 Jan 04 2024 01:49:06

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

%T 3,7,1,2,3,7,2,7,2,6,5,4,1,8,1,6,3,6,2,5,4,5,2,2,1,12,2,4,4,6,4,8,1,4,

%U 3,6,1,8,1,2,5,3,2,6,1,8,2,3,1,9,2,3,2,6,1,9,2,5,3,2,2,9,1,3,4,9,2,7,2,7,7

%N Number of divisors of n with largest digit <= 6 (base 10).

%F a(n) = A083900(n) + A083893(n) = A083902(n) - A083894(n).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A007093(k) = 7.32338572355014919630... . - _Amiram Eldar_, Jan 04 2024

%t a[n_] := DivisorSum[n, 1 &, Max[IntegerDigits[#]] <= 6 &]; Array[a, 100] (* _Amiram Eldar_, Jan 04 2024 *)

%Y Cf. A054055, A000005, A007093, A083893, A083894, A083900, A083902.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, May 08 2003