A174683 Denominator of 1/16 - 1/n^2.

0, 16, 16, 144, 16, 400, 144, 784, 64, 1296, 400, 1936, 18, 2704, 784, 3600, 256, 4624, 1296, 5776, 50, 7056, 1936, 8464, 576, 10000, 2704, 11664, 49, 13456, 3600, 15376, 1024, 17424, 4624, 19600, 81, 21904, 5776, 24336, 1600, 26896, 7056, 29584, 242, 32400, 8464, 35344, 2304, 38416

Offset: 0

Author

Paul Curtz, Nov 30 2010

Keywords

• nonn
• easy
• frac

Comments

The value of a(n)=0 is substituted at the pole n=0.

Extends the Bracket spectrum to negative quantum numbers in the fashion of A061038 (1/4-1/n^2) and A181759 (1/9-1/n^2).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf A174680 (numerators).

Programs

Mathematica

Table[If[n == 0, 0, If[n == 4, 16, Denominator[(n^2 - 16)/(4*n)^2]]], {n, 0, 100}] (* G. C. Greubel, Sep 16 2018 *)
Table[Which[n==0,0,n==4,16,True,Denominator[(n^2-16)/(16n^2)]],{n,0,100}] (* Harvey P. Dale, Dec 13 2024 *)

PARI

for(n=0,100, print1(if(n==0,0, if(n==4,16, denominator((n^2 - 16)/(4*n)^2))), ", ")) \\ G. C. Greubel, Sep 16 2018

Formula

a(n) = A061042(n), n>=4.

a(n) = LCM[n^2 - 16, 16*n^2]/(n^2 - 16), for n>=5. - G. C. Greubel, Sep 16 2018

Extensions

Removed a(-4)-a(-1) since a(-n)=a(n) by G. C. Greubel, Sep 16 2018