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Compound filter (multiplicative order of 2 mod 2n+1 & prime signature of 2n+1): a(n) = P(A002326(n), A046523(2n+1)), where P(n,k) is sequence A000027 used as a pairing function.
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%I #7 Oct 02 2017 18:58:43

%S 1,5,14,9,42,65,90,40,44,189,61,77,273,318,434,20,115,148,702,148,230,

%T 119,265,299,297,86,1430,320,271,1769,1890,142,148,2277,373,665,54,

%U 485,625,819,2400,3485,86,556,77,148,115,856,1224,850,5150,1377,832,5777,702,856,434,1220,265,430,6438,320,5771,35,185,8645,271

%N Compound filter (multiplicative order of 2 mod 2n+1 & prime signature of 2n+1): a(n) = P(A002326(n), A046523(2n+1)), where P(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A292249/b292249.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = (1/2)*(2 + ((A002326(n) + A046523(2n+1))^2) - A002326(n) - 3*A046523(2n+1)).

%o (PARI)

%o A002326(n) = if(n<0, 0, znorder(Mod(2, 2*n+1))); \\ This function from _Michael Somos_, Mar 31 2005

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from _Charles R Greathouse IV_, Aug 17 2011

%o A292249(n) = (1/2)*(2 + ((A002326(n)+A046523(n+n+1))^2) - A002326(n) - 3*A046523(n+n+1));

%o (Scheme) (define (A292249 n) (* 1/2 (+ (expt (+ (A002326 n) (A046523 (+ 1 n n))) 2) (- (A002326 n)) (- (* 3 (A046523 (+ 1 n n)))) 2)))

%Y Cf. A000027, A002326, A046523, A278223, A286573, A291769 (rgs-version of the same filter).

%Y Cf. also A291755, A292268.

%K nonn

%O 0,2

%A _Antti Karttunen_, Oct 02 2017