A054009 n read modulo (number of proper divisors of n).

0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 2, 0, 2, 0, 0, 0, 3, 0, 0, 0, 1, 0, 3, 1, 2, 0, 3, 0, 2, 0, 2, 0, 1, 2, 4, 0, 2, 0, 5, 0, 0, 0, 4, 0, 1, 0, 3, 1, 0, 0, 2, 0, 5, 1, 0, 0, 1, 0, 5, 0, 2, 3, 4, 2, 3, 0, 3, 0, 0, 0, 6, 0, 2, 0, 1, 2, 1, 0, 8, 1, 1, 0, 7, 1, 2, 0, 4, 0, 2, 1, 2, 0, 1, 2, 8, 0, 3, 4, 4, 0, 4, 0, 6, 0, 1

Offset: 2

Author

Asher Auel, Jan 12 2000

Keywords

• nonn

Crossrefs

Cf. A000005, A032741, A054008.

Programs

Maple

[ seq( i mod (tau(i) - 1), i=2..150) ];

Mathematica

Table[Mod[n,DivisorSigma[0,n]-1],{n,2,110}] (* Harvey P. Dale, Dec 05 2015 *)

PARI

a(n) = n % (numdiv(n) - 1); \\ Michel Marcus, Nov 21 2019

Python

from sympy import divisor_count
def A054009(n): return n%(divisor_count(n)-1) # Chai Wah Wu, Mar 14 2023

Formula

a(n) = n mod (tau(n) - 1), for n>1.