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

2,7

Links

Table of n, a(n) for n=2..106.

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000005, A032741, A054008.

Sequence in context: A051632 A278700 A122821 * A339210 A176451 A091297

Adjacent sequences: A054006 A054007 A054008 * A054010 A054011 A054012

Keyword

nonn

Author

Asher Auel, Jan 12 2000

Status

approved