A158622 Numerator of the reduced fraction A158620(n)/A158621(n).
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
Offset: 2
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 2..1000
Programs
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Maple
A158622 := proc(n) 2*(n^2+n+1)/3/n/(n+1) ; numer(%) ; end: seq(A158622(n),n=2..100) ; # R. J. Mathar, Mar 27 2009
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Mathematica
Table[Product[k^3-1,{k,2,n}]/Product[k^3+1,{k,2,n}],{n,2,60}]//Numerator (* Harvey P. Dale, Feb 26 2020 *)
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).
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
Extensions
More terms from R. J. Mathar, Mar 27 2009
Comments