A083888 - OEIS

A083888

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

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, 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, 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

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OFFSET

1,10

LINKS

Robert Israel,Table of n, a(n) for n = 1..10000

FORMULA

a(n) =A000005(n) -A083889(n) -A083890(n) -A083891(n) -A083892(n) -A083893(n) -A083894(n) -A083895(n) -A083896(n).

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

EXAMPLE

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.

MAPLE

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

d:= 1:

map(f, [$1..200]); #Robert Israel,Oct 06 2019

MATHEMATICA

With[{k = 1}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (*Michael De Vlieger,Oct 06 2019 *)

PROG

(Magma) [#[d:d in Divisors(n) | Max(Intseq(d)) eq 1]: n in [1..110]]; //Marius A. Burtea,Oct 06 2019

CROSSREFS

Cf.A054055,A000005,A007088,A083889,A083890,A083891,A083892,A083893,A083894,A083895,A083896.

Sequence in context:A370958 A335208 A165735*A102681 A274013 A172086

Adjacent sequences:A083885 A083886 A083887*A083889 A083890 A083891

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller,May 08 2003

STATUS

approved