A083891 Number of divisors of n with largest digit = 4 (base 10).

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

Offset: 1

Author

Reinhard Zumkeller, May 08 2003

Keywords

• nonn
• base

Examples

			n=120, 3 of the 16 divisors of 120 have largest digit=4: {4,24,40}, therefore a(120)=3.
		

Links

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

Crossrefs

Cf. A054055, A000005, A083899, A277966.

Programs

Maple

ld4:= n -> max(convert(n,base,10)) = 4:
f:= n -> nops(select(ld4,numtheory:-divisors(n))):
map(f, [$1..100]); # Robert Israel, May 02 2019

Mathematica

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]==4&)],{n,110}] (* _Harvey P. Dale, Feb 19 2016 *)

Formula

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083899(n) - A083898(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A277966(k) = 0.98827280431174433126... . - Amiram Eldar, Jan 04 2024