This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A083896 #17 Apr 17 2025 08:09:05
%S A083896 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,
%T A083896 0,1,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0,0,0,
%U A083896 1,0,0,1,0,0,0,1,0,1,1,0,1,0,0,0,0,0,1,0,1,2,1,1,1,1,2,1,1,2,2,0,0,0,0,0,0
%N A083896 Number of divisors of n with largest digit = 9 (base 10).
%H A083896 Robert Israel, <a href="/A083896/b083896.txt">Table of n, a(n) for n = 1..10000</a>
%F A083896 a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) = A000005(n) - A083903(n).
%F A083896 Sum_{k=1..n} a(k) ~ n * (log(n) + c), where c = 2*A001620 - 1 - A082838 = -22.766245... . - _Amiram Eldar_, Apr 17 2025
%e A083896 n = 117, 2 of the 6 divisors of 117 have largest digit = 9: {9,39}, therefore a(117) = 2.
%p A083896 f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
%p A083896 d:= 9:
%p A083896 map(f, [$1..200]); # _Robert Israel_, Oct 06 2019
%t A083896 Table[Count[Divisors[n],_?(Max[IntegerDigits[#]]==9&)],{n,110}] (* _Harvey P. Dale_, Mar 15 2018 *)
%Y A083896 Cf. A054055, A000005, A083888, A083889, A083890, A083891, A083892, A083893, A083894, A083895.
%Y A083896 Cf. A001620, A082838.
%K A083896 nonn,base
%O A083896 1,90
%A A083896 _Reinhard Zumkeller_, May 08 2003