A083892 Number of divisors of n with largest digit = 5 (base 10).

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 1, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 1, 0, 1, 4

Offset

1,15

Links

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

Formula

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083900(n) - A083899(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283608(k) = 1.32926350368137107677... . - Amiram Eldar, Jan 04 2024

Example

n=125, 3 of the 4 divisors of 125 have largest digit =5: {5,25,125}, therefore a(125)=3.

Maple

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 5:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Mathematica

Table[Count[Divisors[n], _?(Max[IntegerDigits[#]]==5&)], {n, 110}] (* Harvey P. Dale, Aug 08 2015 *)

Prog

[#[d:d in Divisors(n) | Max(Intseq(d)) eq 5]: n in [1..150]]; // Marius A. Burtea, Oct 06 2019

Crossrefs

Cf. A054055, A000005, A083900, A083888, A083889, A083890, A083891, A083893, A083894, A083895, A083896, A283608.

Sequence in context: A318950 A319000 A083915 * A354451 A089814 A374205

Adjacent sequences: A083889 A083890 A083891 * A083893 A083894 A083895

Keyword

nonn,base

Author

Reinhard Zumkeller, May 08 2003

Status

approved