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A158622 Numerator of the reduced fraction A158620(n)/A158621(n). 4
7, 13, 7, 31, 43, 19, 73, 91, 37, 133, 157, 61, 211, 241, 91, 307, 343, 127, 421, 463, 169, 553, 601, 217, 703, 757, 271, 871, 931, 331, 1057, 1123, 397, 1261, 1333, 469, 1483, 1561, 547, 1723, 1807, 631, 1981, 2071, 721, 2257, 2353, 817, 2551, 2653, 919, 2863 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

A158620(n) = PRODUCT[k=2..n](k^3-1). A158621(n) = PRODUCT[k=2..n](k^3+1). A158622(n) is the numerator of the reduced fraction A158620(n)/A158621(n). A158623(n) is the denominator of the reduced fraction A158620(n)/A158621(n). The reduced fractions are 7/9, 13/18, 7/10, 31/45, 43/63, 19/28, 73/108, 91/135, 37/55, 133/198, ...

Is this the same as A046163? [From R. J. Mathar, Mar 27 2009]

Apparently a(n) = A130770(n) for 2 <= n <= 53. - Georg Fischer, Oct 24 2018

LINKS

Table of n, a(n) for n=2..53.

FORMULA

numerator of (PRODUCT[k=2..n](k^3-1))/PRODUCT[k=2..n](k^3+1) = numerator of PRODUCT[k=2..n]A068601(k)/A001093(k).

A158620(n)/A158621(n) = 2(n^2+n+1)/(3n(n+1)). [From R. J. Mathar, Mar 27 2009]

Empirical g.f.: -x^2*(x^8+x^7+x^6-2*x^5+4*x^4+10*x^3+7*x^2+13*x+7) / ((x-1)^3*(x^2+x+1)^3). - Colin Barker, May 09 2013

EXAMPLE

a(2) = 7 = numerator of (2^3-1)/2^3+1 = 7/9. a(3) = 13 = numerator of ((2^3-1)*(3^3-1))/((2^3+1)*(3^3+1)) = (7 * 26)/ (9 * 28) = 182/252 = 13/18. a(4) = 7 = = numerator of ((2^3-1)*(3^3-1)*(4^3-1))/((2^3+1)*(3^3+1)*(4^3+1)) = (7 * 26 * 63)/(9 * 28 * 65) = 11466/16380 = 7/10. a(5) = 31 = numerator of ((2^3-1)(3^3-1)(4^3-1)(5^3-1))/((2^3+1)(3^3+1)(4^3+1)(5^3+1)) = 1421784/2063880 = 31/45.

MAPLE

A158622 := proc(n) 2*(n^2+n+1)/3/n/(n+1) ; numer(%) ; end: seq(A158622(n), n=2..100) ; [From R. J. Mathar, Mar 27 2009]

CROSSREFS

Cf. A001093, A016921, A068601, A130770, A158620-A158621, A158623.

Sequence in context: A081257 A046163 A130770 * A215990 A122874 A066003

Adjacent sequences:  A158619 A158620 A158621 * A158623 A158624 A158625

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Mar 23 2009

EXTENSIONS

More terms from R. J. Mathar, Mar 27 2009

STATUS

approved

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Last modified January 18 07:18 EST 2019. Contains 319269 sequences. (Running on oeis4.)