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

1,6

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A054009, A033950, A066708.

Sequence in context: A335489 A281188 A323439 * A347031 A125676 A291955

Adjacent sequences: A054005 A054006 A054007 * A054009 A054010 A054011

Keyword

nonn

Author

Asher Auel, Jan 12 2000

Status

approved