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A246053 The denominator of h(n-k)*h(k)/h(n) where h(x) = zeta(2*x)*(4^x-2) and k = floor(n/2). 6
2, 2, 7, 62, 381, 365, 1414477, 573370, 118518239, 5749691557, 274638832071, 768018339627, 29741482024668555, 860983513348179, 65053034220152267, 1850237821952082716222, 16555640865486520478399, 962703047799452264039, 29167285342563717499865628061 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

There are terms that are not squarefree. For example, a(113) is divisible by 631^2 and a(114) is divisible by 103^2. Most terms appear to be divisible by numerator(bernoulli(2*n)/factorial(2*n)) but not all. The first two exceptions are a(1437) and a(23766). - Hans Havermann, Aug 16 2014

LINKS

Hans Havermann, Table of n, a(n) for n = 0..200

Hans Havermann, Factorization table of n, a(n) for n = 0..150

Dinesh S. Thakur, A note on numerators of Bernoulli numbers, Proc. Amer. Math. Soc. 140 (2012), 3673-3676.

FORMULA

a(n) = A246052(n, floor(n/2)).

EXAMPLE

a( 0) = 2

a( 1) = 2

a( 2) = 7

a( 3) = 2 * 31

a( 4) = 3 * 127

a( 5) = 5 * 73

a( 6) = 23 * 89 * 691

a( 7) = 2 * 5 * 7 * 8191

a( 8) = 7 * 31 * 151 * 3617

a( 9) = 43867 * 131071

a(10) = 3 * 283 * 617 * 524287

a(11) = 3 * 7 * 11 * 127 * 131 * 337 * 593

a(12) = 3 * 5 * 47 * 103 * 178481 * 2294797

a(13) = 3 * 13 * 31 * 601 * 1801 * 657931

PROG

(Sage)

h = lambda x: zeta(2*x)*(4^x-2)

A246053 = lambda n: Integer((h((n+1)//2)*h(n//2)/h(n)).denominator())

[A246053(n) for n in range(19)]

CROSSREFS

Cf. A242035 (numerator), A240978 (largest prime divisor), A242050, A246051, A246052.

Sequence in context: A298440 A317808 A326909 * A062448 A248237 A139523

Adjacent sequences:  A246050 A246051 A246052 * A246054 A246055 A246056

KEYWORD

nonn,frac

AUTHOR

Peter Luschny, Aug 12 2014

STATUS

approved

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Last modified August 22 11:59 EDT 2019. Contains 326177 sequences. (Running on oeis4.)