A129292 Number of divisors of n^4 - 1 that are not greater than n.

1, 1, 2, 2, 4, 2, 6, 4, 5, 3, 8, 3, 10, 4, 6, 4, 12, 4, 13, 4, 11, 6, 14, 3, 10, 6, 12, 6, 17, 3, 16, 7, 10, 9, 13, 4, 18, 7, 11, 4, 22, 3, 26, 8, 9, 7, 23, 5, 18, 7, 13, 6, 25, 4, 24, 8, 21, 6, 18, 3, 18, 10, 12, 14, 16, 4, 26, 8, 17, 7, 31, 5, 30, 6, 11, 13, 26, 7, 25, 6, 16, 10, 35, 4, 18, 11

Offset

1,3

Comments

a(n) = #{d: d<=n and A123865(n) mod d = 0};

a(n)>1 for n>2, see A129293 for m such that a(m)=2: a(A129293(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) = #{1,3,9,11,33,73,99} = 7.

Maple

f:= n -> nops(select(`<=`, numtheory:-divisors(n^4-1), n)):
1, seq(f(n), n=2..100); # Robert Israel, Sep 21 2014

Mathematica

Table[Count[Divisors[n^4-1], _?(#<=n&)], {n, 90}] (* Harvey P. Dale, Aug 13 2014 *)

Prog

(PARI) a(n) = if (n==1, 1, sumdiv(n^4-1, d, d <= n)); \\ Michel Marcus, Sep 21 2014
(Python)
from itertools import takewhile
from sympy import divisors
def A129292(n): return sum(1 for d in takewhile(lambda x:x<=n, divisors(n**4-1))) if n>1 else 1 # Chai Wah Wu, Mar 19 2026

Crossrefs

Cf. A129294, A129296.

Sequence in context: A091279 A096002 A082175 * A126606 A285699 A278229

Adjacent sequences: A129289 A129290 A129291 * A129293 A129294 A129295

Keyword

nonn

Author

Reinhard Zumkeller, Apr 09 2007

Status

approved