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a(n) = 2*(n*Denominator(((n-1)*(n^2)+2^(n+1)-4)/(2*n))-n)/n+1.
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%I #25 Sep 08 2022 08:46:08

%S 1,1,1,3,1,5,1,7,5,9,1,11,1,13,9,15,1,17,1,19,13,21,1,23,9,25,17,3,1,

%T 29,1,31,21,33,69,35,1,37,25,39,1,41,1,43,5,45,1,47,13,49,33,51,1,53,

%U 109,55,37,57,1,59,1,61,41,63,25,65,1,67,45,9,1,71,1,73,49,75,153,77,1,79

%N a(n) = 2*(n*Denominator(((n-1)*(n^2)+2^(n+1)-4)/(2*n))-n)/n+1.

%C Numbers n such that a(a(n + 1)) = 1: 1 U primes U pseudoprimes;

%C a(n) such that a(n - 1) = 1: 1 U 1 U odd primes U pseudoprimes.

%e a(1) = (2*(1*Denominator(((1-1)*(1^2)+2^(1+1)-4)/(2*1))-1)/1+1 = 1.

%o (Magma) [2*(n*Denominator(((n-1)*(n^2)+2^(n+1)-4)/(2*n))-n)/n+1: n in [1..100]];

%o (PARI) a(n) = 2*(n*denominator(((n-1)*(n^2)+2^(n+1)-4)/(2*n))-n)/n + 1; \\ _Michel Marcus_, Sep 03 2014

%Y Cf. A000040, A001567, A015919, A065091.

%K nonn

%O 1,4

%A _Juri-Stepan Gerasimov_, Sep 01 2014