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A083889 Number of divisors of n with largest digit = 2 (base 10).

%I A083889 #23 Jan 04 2024 03:23:20
%S A083889 0,1,0,1,0,1,0,1,0,1,0,2,0,1,0,1,0,1,0,2,1,2,0,2,0,1,0,1,0,1,0,1,0,1,
%T A083889 0,2,0,1,0,2,0,2,0,2,0,1,0,2,0,1,0,1,0,1,0,1,0,1,0,3,0,1,1,1,0,2,0,1,
%U A083889 0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,2,0,2,0,1,1
%N A083889 Number of divisors of n with largest digit = 2 (base 10).
%H A083889 Robert Israel, <a href="/A083889/b083889.txt">Table of n, a(n) for n = 1..10000</a>
%F A083889 a(n) = A000005(n) - A083888(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083897(n) - A083888(n).
%F A083889 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A277964(k) = 0.85636382912390578285... . - _Amiram Eldar_, Jan 04 2024
%e A083889 n=120, 4 of the 16 divisors of 120 have largest digit =2: {2,12,20,120}, therefore a(120)=4.
%p A083889 f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
%p A083889 d:= 2:
%p A083889 map(f, [$1..200]); # _Robert Israel_, Oct 06 2019
%t A083889 With[{k = 2}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* _Michael De Vlieger_, Oct 06 2019 *)
%o A083889 (Magma) [#[d:d in Divisors(n) | Max(Intseq(d)) eq 2]: n in [1..120]]; // _Marius A. Burtea_, Oct 06 2019
%Y A083889 Cf. A054055, A000005, A083897, A083888, A083890, A083891, A083892, A083893, A083894, A083895, A083896, A277964.
%K A083889 nonn,base
%O A083889 1,12
%A A083889 _Reinhard Zumkeller_, May 08 2003