A174680 - OEIS

%I #20 Sep 26 2018 21:43:29

%S -1,-15,-3,-7,0,9,5,33,3,65,21,105,1,153,45,209,15,273,77,345,3,425,

%T 117,513,35,609,165,713,3,825,221,945,63,1073,285,1209,5,1353,357,

%U 1505,99,1665,437,1833,15,2009,525,2193,143,2385,621,2585,21,2793,725,3009,195,3233,837,3465,14,3705

%N Numerator of 1/16 - 1/n^2, using -1 at the pole where n=0.

%C Extends the Brackett spectrum to negative principal quantum numbers in the spirit of A144477 and A171709.

%H G. C. Greubel, <a href="/A174680/b174680.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A061041(n), n >= 4.

%F a(n) = A172157(4,n), n >= 1.

%F a(n) = a(-n) for all n in Z.

%t Table[(n^2 - 16)/(GCD[n^2 - 16, 16*n^2]), {n, 0, 100}] (* _G. C. Greubel_, Sep 16 2018 *)

%o (PARI) {a(n) = (n^2 - 16) / gcd(n^2 - 16, 16 * n^2)}; /* _Michael Somos_, Jan 06 2011 */

%Y Cf. A174233, A067998.

%K sign,easy

%O 0,2

%A _Paul Curtz_, Nov 30 2010

%E removed a(-4)-a(-1) since a(-n)=a(n) by _Michael Somos_, Jan 06 2011