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Number of divisors of n with the largest digit of the divisor <= 7 (base 10).
4

%I #9 Jan 04 2024 01:49:23

%S 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,

%T 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,

%U 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

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

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

%F 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

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

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

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, May 08 2003

%E Definition clarified by _Harvey P. Dale_, Nov 01 2022