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

1,24

Links

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

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

Example

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

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 *)

Crossrefs

Cf. A054055, A000005, A083899, A277966.

Sequence in context: A325433 A167688 A083914 * A363860 A087623 A265260

Adjacent sequences: A083888 A083889 A083890 * A083892 A083893 A083894

Keyword

nonn,base

Author

Reinhard Zumkeller, May 08 2003

Status

approved