%I #17 Jan 04 2024 03:23:55

%S 0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,2,0,0,0,2,0,0,0,1,0,1,

%T 0,1,0,0,0,2,1,2,1,2,0,0,0,2,0,0,0,1,0,0,0,2,0,0,0,1,0,0,0,1,0,0,0,2,

%U 0,1,0,2,0,0,0,1,0,0,0,2,0,1,0,3,0,1,0,2,0,0,0,1,0,0,0,2,0,1,0,1,0,1,0,2,0

%N Number of divisors of n with largest digit = 4 (base 10).

%H Robert Israel, <a href="/A083891/b083891.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083899(n) - A083898(n).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A277966(k) = 0.98827280431174433126... . - _Amiram Eldar_, Jan 04 2024

%e n=120, 3 of the 16 divisors of 120 have largest digit=4: {4,24,40}, therefore a(120)=3.

%p ld4:= n -> max(convert(n,base,10)) = 4:

%p f:= n -> nops(select(ld4,numtheory:-divisors(n))):

%p map(f, [$1..100]); # _Robert Israel_, May 02 2019

%t Table[Count[Divisors[n],_?(Max[IntegerDigits[#]]==4&)],{n,110}] (* _Harvey P. Dale_, Feb 19 2016 *)

%Y Cf. A054055, A000005, A083899, A277966.

%K nonn,base

%O 1,24

%A _Reinhard Zumkeller_, May 08 2003