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%I #20 Jan 04 2024 03:24:24
%S 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,
%T 0,1,0,1,0,1,0,0,0,0,0,0,0,2,0,0,0,0,0,1,0,2,0,1,0,0,0,0,0,1,0,0,0,1,
%U 0,0,0,2,0,0,0,1,0,1,0,2,1,1,1,2,1,1,1,2,0,1,0,0,0,0,0,2,0,0,0,0,0,0,0,1,0
%N Number of divisors of n with largest digit = 8 (base 10).
%H Robert Israel, <a href="/A083895/b083895.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083896(n) = A083903(n) - A083902(n).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283611(k) = 11.62909500243165896645... . - _Amiram Eldar_, Jan 04 2024
%e n=72, 2 of the 12 divisors of 72 have largest digit =8: {8,18}, therefore a(72)=2.
%p f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
%p d:= 8:
%p map(f, [$1..200]); # _Robert Israel_, Oct 06 2019
%t With[{k = 8}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* _Michael De Vlieger_, Oct 06 2019 *)
%Y Cf. A054055, A000005, A083903, A083888, A083889, A083890, A083891, A083892, A083893, A083894, A083896, A283611.
%K nonn,base
%O 1,48
%A _Reinhard Zumkeller_, May 08 2003
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