cp's OEIS Frontend

A083888 Number of divisors of n with largest digit = 1 (base 10).

%I A083888 #20 Jan 04 2024 01:43:09
%S A083888 1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,2,1,1,2,1,
%T A083888 1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,1,
%U A083888 1,2,1,1,1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,2,3,2,1,1,1,1
%N A083888 Number of divisors of n with largest digit = 1 (base 10).
%H A083888 Robert Israel, <a href="/A083888/b083888.txt">Table of n, a(n) for n = 1..10000</a>
%F A083888 a(n) = A000005(n) - A083889(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n).
%F A083888 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A007088(k) = 1.23840561530559480971... . - _Amiram Eldar_, Jan 04 2024
%e A083888 n=110, 4 of the divisors of 110 {1,2,5,10,11,22,55,110} have largest digit =1: {1,10,11,110}, therefore a(110)=4.
%p A083888 f:= proc(n) nops(select(t -> max(convert(t,base,10))=d, numtheory:-divisors(n))) end proc:
%p A083888 d:= 1:
%p A083888 map(f, [$1..200]); # _Robert Israel_, Oct 06 2019
%t A083888 With[{k = 1}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* _Michael De Vlieger_, Oct 06 2019 *)
%o A083888 (Magma) [#[d:d in Divisors(n) | Max(Intseq(d)) eq 1]: n in [1..110]]; // _Marius A. Burtea_, Oct 06 2019
%Y A083888 Cf. A054055, A000005, A007088, A083889, A083890, A083891, A083892, A083893, A083894, A083895, A083896.
%K A083888 nonn,base
%O A083888 1,10
%A A083888 _Reinhard Zumkeller_, May 08 2003