A083894 Number of divisors of n with largest digit = 7 (base 10).

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

Offset

1,70

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) - A083895(n) - A083896(n) = A083902(n) - A083901(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283610(k) = 3.96819589328234218540... . - Amiram Eldar, Jan 04 2024

Example

n=119, 2 of the 4 divisors of 119 have largest digit =7: {7,17}, therefore a(119)=2.

Maple

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 7:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Mathematica

Table[Count[Divisors[n], _?(Max[IntegerDigits[#]]==7&)], {n, 120}] (* Harvey P. Dale, Oct 16 2021 *)

Crossrefs

Cf. A054055, A000005, A083902, A083888, A083889, A083890, A083891, A083892, A083893, A083895, A083896, A283610.

Sequence in context: A165983 A300719 A341998 * A128257 A198254 A309059

Adjacent sequences: A083891 A083892 A083893 * A083895 A083896 A083897

Keyword

nonn,base

Author

Reinhard Zumkeller, May 08 2003

Status

approved