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A335949 a(n) = denominator(b_n(x)), where b_n(x) are the polynomials defined in A335947. 2
1, 1, 12, 4, 240, 48, 1344, 192, 3840, 1280, 33792, 3072, 5591040, 430080, 245760, 49152, 16711680, 983040, 522977280, 27525120, 1211105280, 173015040, 1447034880, 62914560, 22900899840, 4580179968, 1409286144, 469762048, 116769423360, 4026531840, 7689065201664 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequence can also be computed without reference to the Bernoulli polynomials (ultimately thanks to the von Staudt-Clausen theorem) by the method of Kellner and Sondow (2019). Compare the SageMath program.

LINKS

Table of n, a(n) for n=0..30.

Bernd C. Kellner and Jonathan Sondow, On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits, arXiv:1902.10672 [math.NT], 2019.

FORMULA

a(n) = min {m | m*([x^k] b(n, x)) is integer for all k = 0..n}.

The odd part of a(n) is squarefree (A000265).

a(n) and A144845(n) have the same odd prime factors.

a(n)/A144845(n) = 4^floor(n/2)/2 for n >= 1.

a(n)/rad(a(n)) = A158302(n+1), (rad=A007947).

PROG

(SageMath)

def A335949(n):

a = set(prime_divisors(n + 1)) - set([2])

b = (

p

for p in prime_range(3, (n + 2) // (2 + n % 2))

if not p.divides(n + 1) and sum((n + 1).digits(base=p)) >= p

)

p = list(a.union(set(b)))

return 4 ^ (n // 2) * mul(p)

print([A335949(n) for n in range(31)])

CROSSREFS

Cf. A335947/A335948, A144845, A158302.

Sequence in context: A144630 A107670 A157782 * A002679 A282578 A205141

Adjacent sequences: A335946 A335947 A335948 * A335950 A335951 A335952

KEYWORD

nonn

AUTHOR

Peter Luschny, Jul 01 2020

STATUS

approved

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Last modified December 2 20:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)