A195155 Number of divisors d of n such that d-1 also divides n or d-1 = 0.

1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 3, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 6, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 5, 1, 2

Offset

1,2

Comments

First differs from A055874 at a(20).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A000005(n) - A195150(n).

a(n) = 1 + A129308(n).

a(2n-1) = 1; a(2n) = 1 + A007862(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - Amiram Eldar, Dec 31 2023

Maple

with(numtheory):
a:= n-> add(`if`(d=1 or irem(n, d-1)=0, 1, 0), d=divisors(n)):
seq(a(n), n=1..200);  # Alois P. Heinz, Oct 17 2011

Mathematica

d1[n_]:=Module[{d=Rest[Divisors[n]]}, Count[d, _?(Divisible[n, #-1]&)]+1]; Array[d1, 90] (* Harvey P. Dale, Oct 31 2013 *)

Crossrefs

Cf. A000005, A007862, A049820, A055874, A129308, A137921, A195150, A195153.

Sequence in context: A204917 A232098 A055874 * A178544 A161506 A066451

Adjacent sequences: A195152 A195153 A195154 * A195156 A195157 A195158

Keyword

nonn

Author

Omar E. Pol, Sep 19 2011

Status

approved