|
%I #31 Jan 04 2024 01:46:43
%S 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,
%T 0,2,0,0,0,0,0,1,0,0,0,1,0,2,0,0,0,1,0,1,0,1,0,0,0,2,1,1,1,2,1,2,0,0,
%U 0,0,0,2,0,0,0,0,0,2,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,2,0,0,0,0,0,1,0,1,0
%N Number of divisors of n with largest digit = 6 (base 10).
%H Robert Israel, <a href="/A083893/b083893.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) - A083894(n) - A083895(n) - A083896(n) = A083901(n) - A083900(n).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283609(k) = 2.06890539387954414920... . - _Amiram Eldar_, Jan 04 2024
%e n=240, 3 of the 20 divisors of 240 have largest digit =6: {6,16,60}, therefore a(240)=3.
%p f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
%p d:= 6:
%p map(f, [$1..200]); # _Robert Israel_, Oct 06 2019
%t With[{k = 6}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* _Michael De Vlieger_, Oct 06 2019 *)
%o (Magma) [#[d:d in Divisors(n) | Max(Intseq(d)) eq 6]: n in [1..150]]; // _Marius A. Burtea_, Oct 06 2019
%Y Cf. A054055, A000005, A083901, A083888, A083889, A083890, A083891, A083892, A083894, A083895, A083896, A283609.
%K nonn,base
%O 1,36
%A _Reinhard Zumkeller_, May 08 2003
|
