A054008 n read modulo (number of divisors of n).

0, 0, 1, 1, 1, 2, 1, 0, 0, 2, 1, 0, 1, 2, 3, 1, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 1, 8, 1, 2, 3, 4, 1, 6, 3, 0, 1, 2, 1, 0, 1, 2, 3, 1, 1, 2, 1, 2, 1, 6, 1, 0, 1, 2, 3, 4, 1, 6, 1, 0, 1, 2, 1, 0, 1, 2, 3, 0, 1, 6, 3, 2, 1, 2, 3, 0, 1, 2, 3, 1, 1, 6, 1, 0, 1

Offset: 1

Author

Asher Auel, Jan 12 2000

Keywords

• nonn

Comments

a(n)=0 iff n is a refactorable number (cf. A033950). - Franz Vrabec, Oct 16 2005

a(A066708(n)) = n and a(m) < n for m < A066708(n). - Reinhard Zumkeller, Sep 17 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A054009, A033950, A066708.

Programs

Haskell

a054008 n = n `mod` a000005 n  -- Reinhard Zumkeller, Sep 17 2014

Maple

[ seq( i mod tau(i), i=1..130) ];

Mathematica

a[n_] := Mod[n, DivisorSigma[0, n]]; Array[a, 105] (* Jean-François Alcover, Sep 19 2017 *)

PARI

a(n) = n % numdiv(n); \\ Michel Marcus, Sep 19 2017

Python

from sympy import divisor_count
def A054008(n): return n%divisor_count(n) # Chai Wah Wu, Mar 14 2023

Formula

a(n) = n mod tau(n).