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A335949
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a(n) = denominator(b_n(x)), where b_n(x) are the polynomials defined in A335947.
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2
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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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.
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FORMULA
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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).
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PROG
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(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)])
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CROSSREFS
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Cf. A335947/A335948, A144845, A158302.
Sequence in context: A144630 A107670 A157782 * A002679 A282578 A205141
Adjacent sequences: A335946 A335947 A335948 * A335950 A335951 A335952
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KEYWORD
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nonn
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AUTHOR
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Peter Luschny, Jul 01 2020
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STATUS
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approved
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