A083893 Number of divisors of n with largest digit = 6 (base 10).

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

Offset

1,36

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) - A083894(n) - A083895(n) - A083896(n) = A083901(n) - A083900(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283609(k) = 2.06890539387954414920... . - Amiram Eldar, Jan 04 2024

Example

n=240, 3 of the 20 divisors of 240 have largest digit =6: {6,16,60}, therefore a(240)=3.

Maple

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 6:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Mathematica

With[{k = 6}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* Michael De Vlieger, Oct 06 2019 *)

Prog

(Magma) [#[d:d in Divisors(n) | Max(Intseq(d)) eq 6]: n in [1..150]]; // Marius A. Burtea, Oct 06 2019

Crossrefs

Cf. A054055, A000005, A083901, A083888, A083889, A083890, A083891, A083892, A083894, A083895, A083896, A283609.

Sequence in context: A341618 A337690 A083916 * A187097 A094428 A277148

Adjacent sequences: A083890 A083891 A083892 * A083894 A083895 A083896

Keyword

nonn,base

Author

Reinhard Zumkeller, May 08 2003

Status

approved