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A291755 Compound filter (multiplicative order of 2 mod 2n+1 & eulerphi(2n+1)): a(n) = P(A002326(n), A037225(n)), where P(n,k) is sequence A000027 used as a pairing function.

%I A291755 #14 Nov 23 2024 11:27:47
%S A291755 1,5,25,31,61,181,265,59,261,613,142,507,761,613,1513,566,416,607,
%T A291755 2521,607,1731,1499,607,2301,1912,749,5305,1731,1396,6613,7081,826,
%U A291755 1723,8581,2102,5391,3169,1731,3946,6709,5725,13285,2493,3431,4764,3415,2356,5707,10201,3946,19801,11527
%N A291755 Compound filter (multiplicative order of 2 mod 2n+1 & eulerphi(2n+1)): a(n) = P(A002326(n), A037225(n)), where P(n,k) is sequence A000027 used as a pairing function.
%H A291755 Antti Karttunen, <a href="/A291755/b291755.txt">Table of n, a(n) for n = 0..10000</a>
%F A291755 a(n) = (1/2)*(2 + ((A002326(n) + A000010(2n+1))^2) - A002326(n) - 3*A000010(2n+1)).
%t A291755 A002326[n_] := MultiplicativeOrder[2, 2n+1];
%t A291755 a[n_] := (1/2)*(2 + ((A002326[n] + EulerPhi[2n+1])^2) - A002326[n] - 3* EulerPhi[2n+1]);
%t A291755 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Nov 23 2024 *)
%o A291755 (PARI)
%o A291755 A002326(n) = if(n<0, 0, znorder(Mod(2, 2*n+1))); \\ This function from _Michael Somos_, Mar 31 2005
%o A291755 A291755(n) = (1/2)*(2 + ((A002326(n)+eulerphi(n+n+1))^2) - A002326(n) - 3*eulerphi(n+n+1));
%o A291755 (Scheme) (define (A291755 n) (* 1/2 (+ (expt (+ (A002326 n) (A000010 (+ 1 n n))) 2) (- (A002326 n)) (- (* 3 (A000010 (+ 1 n n)))) 2)))
%Y A291755 Cf. A000010, A000027, A002326, A037225, A291766 (rgs-version of this filter).
%Y A291755 Cf. also A292249, A292268.
%Y A291755 Cf. A037226, A053006.
%K A291755 nonn
%O A291755 0,2
%A A291755 _Antti Karttunen_, Oct 02 2017