A083896 Number of divisors of n with largest digit = 9 (base 10).

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

Offset

1,90

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) - A083892(n) - A083893(n) - A083894(n) - A083895(n) = A000005(n) - A083903(n).

Sum_{k=1..n} a(k) ~ n * (log(n) + c), where c = 2*A001620 - 1 - A082838 = -22.766245... . - Amiram Eldar, Apr 17 2025

Example

n = 117, 2 of the 6 divisors of 117 have largest digit = 9: {9,39}, therefore a(117) = 2.

Maple

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 9:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Mathematica

Table[Count[Divisors[n], _?(Max[IntegerDigits[#]]==9&)], {n, 110}] (* Harvey P. Dale, Mar 15 2018 *)

Crossrefs

Cf. A054055, A000005, A083888, A083889, A083890, A083891, A083892, A083893, A083894, A083895.

Cf. A001620, A082838.

Sequence in context: A357849 A097295 A220572 * A332083 A084115 A284154

Adjacent sequences: A083893 A083894 A083895 * A083897 A083898 A083899

Keyword

nonn,base

Author

Reinhard Zumkeller, May 08 2003

Status

approved