A083889 Number of divisors of n with largest digit = 2 (base 10).

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 1

Offset

1,12

Links

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

Formula

a(n) = A000005(n) - A083888(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083897(n) - A083888(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A277964(k) = 0.85636382912390578285... . - Amiram Eldar, Jan 04 2024

Example

n=120, 4 of the 16 divisors of 120 have largest digit =2: {2,12,20,120}, therefore a(120)=4.

Maple

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 2:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Mathematica

With[{k = 2}, 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 2]: n in [1..120]]; // Marius A. Burtea, Oct 06 2019

Crossrefs

Cf. A054055, A000005, A083897, A083888, A083890, A083891, A083892, A083893, A083894, A083895, A083896, A277964.

Sequence in context: A106404 A292242 A280800 * A360079 A127523 A364389

Adjacent sequences: A083886 A083887 A083888 * A083890 A083891 A083892

Keyword

nonn,base

Author

Reinhard Zumkeller, May 08 2003

Status

approved