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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
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
Sequence in context: A144630 A107670 A157782 * A002679 A282578 A205141
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 01 2020
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)