A129294 Number of divisors of n^3 - 1 that are not greater than n.

1, 1, 2, 2, 3, 2, 4, 2, 5, 3, 5, 2, 7, 2, 4, 7, 5, 3, 6, 2, 6, 6, 6, 2, 13, 4, 4, 4, 8, 4, 10, 3, 6, 5, 6, 5, 14, 2, 6, 5, 8, 3, 10, 3, 8, 10, 5, 3, 16, 3, 9, 5, 9, 2, 11, 5, 8, 7, 4, 3, 20, 2, 5, 9, 11, 4, 18, 4, 6, 5, 8, 3, 14, 5, 4, 8, 6, 4, 17, 2, 21, 5, 6, 3, 16, 6, 10, 8, 8, 2, 14, 5, 9, 7, 6, 5, 16

Offset

1,3

Comments

a(n) = #{d: d<=n and A068601(n) mod d = 0};

a(n)>1 for n>2, see A129295 for m such that a(m)=2: a(A129295(n))=2.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)

Example

a(1) = #{1} = 1.
a(100) = #{1,3,7,9,11,13,21,27,33,37,39,63,77,91,99} = 15.

Mathematica

Table[Count[Divisors[n^3-1], _?(#<n+1&)], {n, 2, 100}] (* Harvey P. Dale, Sep 27 2018 *)

Prog

(PARI) a(n) = sumdiv(n^3-1, d, d <= n); \\ Michel Marcus, Aug 01 2018
(Python)
from itertools import takewhile
from sympy import divisors
def A129294(n): return sum(1 for d in takewhile(lambda x:x<=n, divisors(n**3-1))) if n>1 else 1 # Chai Wah Wu, Mar 19 2026

Crossrefs

Cf. A129292, A129296.

Sequence in context: A370816 A305813 A319355 * A363719 A363723 A350126

Adjacent sequences: A129291 A129292 A129293 * A129295 A129296 A129297

Keyword

nonn

Author

Reinhard Zumkeller, Apr 09 2007

Status

approved