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A083894 Number of divisors of n with largest digit = 7 (base 10). 12

%I #18 Jan 04 2024 03:24:11

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

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

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

%N Number of divisors of n with largest digit = 7 (base 10).

%H Robert Israel, <a href="/A083894/b083894.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) - A083895(n) - A083896(n) = A083902(n) - A083901(n).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283610(k) = 3.96819589328234218540... . - _Amiram Eldar_, Jan 04 2024

%e n=119, 2 of the 4 divisors of 119 have largest digit =7: {7,17}, therefore a(119)=2.

%p f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:

%p d:= 7:

%p map(f, [$1..200]); # _Robert Israel_, Oct 06 2019

%t Table[Count[Divisors[n],_?(Max[IntegerDigits[#]]==7&)],{n,120}] (* _Harvey P. Dale_, Oct 16 2021 *)

%Y Cf. A054055, A000005, A083902, A083888, A083889, A083890, A083891, A083892, A083893, A083895, A083896, A283610.

%K nonn,base

%O 1,70

%A _Reinhard Zumkeller_, May 08 2003

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)