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A129296 Number of divisors of n^2 - 1 that are not greater than n. 5
1, 1, 2, 2, 4, 2, 5, 3, 5, 3, 8, 2, 8, 4, 6, 4, 9, 2, 12, 4, 8, 4, 10, 3, 10, 6, 8, 4, 16, 2, 14, 4, 7, 8, 12, 4, 12, 4, 10, 4, 20, 2, 16, 6, 8, 6, 12, 3, 18, 6, 12, 4, 16, 4, 20, 8, 10, 4, 16, 2, 16, 6, 8, 12, 16, 4, 16, 4, 16, 4, 30, 2, 15, 6, 8, 12, 16, 4, 24, 5, 12, 5, 16, 4, 16, 8, 10, 4, 30, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = #{d: d<=n and A005563(n+1) mod d = 0};

a(n)>1 for n>2, see A129297 for m such that a(m)=2: a(A129297(n))=2.

If a(6n)==2 for n>=1, then 6n-1 and 6n+1 are twin primes see A129297. - Fred Daniel Kline, Jan 02 2014

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

Adrian Dudek, On the Number of Divisors of n^2-1, arXiv:1507.08893 [math.NT], 2015.

FORMULA

a(n) = A000005(n^2-1)/2 for n >= 2. - Robert Israel, Aug 03 2015

EXAMPLE

a(100) = #{1,3,9,11,33,99} = 6.

MAPLE

1, seq(numtheory:-tau(n^2-1)/2, n=2..100); # Robert Israel, Aug 03 2015

MATHEMATICA

nd[n_]:=Count[Divisors[n^2-1], _?(#<=n&)]; Array[nd, 100] (* Harvey P. Dale, Jan 03 2014 *)

PROG

(PARI) a(n) = if (n==1, 1, sumdiv(n^2-1, d, d<=n)); \\ Michel Marcus, Jan 02 2014

(Haskell)

a129296 n = length [d | d <- [1..n], (n ^ 2 - 1) `mod` d == 0]

-- Reinhard Zumkeller, Jan 09 2014

CROSSREFS

Cf. A129292, A129294.

Sequence in context: A217895 A005128 A187782 * A300837 A321443 A125296

Adjacent sequences:  A129293 A129294 A129295 * A129297 A129298 A129299

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 09 2007

STATUS

approved

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Last modified September 17 06:00 EDT 2019. Contains 327119 sequences. (Running on oeis4.)