%I #25 Oct 26 2012 02:33:09

%S 1,2,3,2,1,1,1,2,3,5,1,1,1,1,1,2,1,1,1,1,7,1,1,1,1,1,3,1,1,1,1,2,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,11,1,1,1,1,1,1,1,1,2,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,13

%N a(A130290(n) * A000040(n)^n1) = A000040(n), n >= 1 and n1 >= 1, and a(n) = 1 elsewhere.

%C The a(n) are related to the prime numbers A000040 and the number of nonzero quadratic residues modulo the n-th prime A130290, see the first formula and the Maple program.

%C This sequence resembles the exponential of the von Mangoldt function A014963; for the latter sequence a(A000040(n)^n1) = A000040(n), n >= 1 and n1 >= 1, and a(n) = 1 elsewhere.

%F a(A130290(n) * A000040(n)^n1) = A000040(n), n >= 1 and n1 >= 1, and a(n)= 1 elsewhere.

%F a(n) = (A160479(n+1) * A128060(n+1))/(2*n+1) for n >= 2.

%p nmax := 78: A000040 := proc(n): ithprime(n) end: A130290 := proc(n): if n =1 then 1 else (A000040(n)-1)/2 fi: end: for n from 1 to nmax do A217983(n) := 1 od: for n from 1 to nmax do for n1 from 1 to floor(log[A000040(n)](nmax)) do A217983(A130290(n) * A000040(n)^n1) := A000040(n) od: od: seq(A217983(n), n=1..nmax);

%K nonn

%O 1,2

%A _Johannes W. Meijer_, Oct 25 2012