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.

1, 5, 25, 31, 61, 181, 265, 59, 261, 613, 142, 507, 761, 613, 1513, 566, 416, 607, 2521, 607, 1731, 1499, 607, 2301, 1912, 749, 5305, 1731, 1396, 6613, 7081, 826, 1723, 8581, 2102, 5391, 3169, 1731, 3946, 6709, 5725, 13285, 2493, 3431, 4764, 3415, 2356, 5707, 10201, 3946, 19801, 11527

Offset: 0

Author

Antti Karttunen, Oct 02 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000010, A000027, A002326, A037225, A291766 (rgs-version of this filter).

Cf. also A292249, A292268.

Cf. A037226, A053006.

Programs

Mathematica

A002326[n_] := MultiplicativeOrder[2, 2n+1];
a[n_] := (1/2)*(2 + ((A002326[n] + EulerPhi[2n+1])^2) - A002326[n] - 3* EulerPhi[2n+1]);
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 23 2024 *)

PARI

A002326(n) = if(n<0, 0, znorder(Mod(2, 2*n+1))); \\ This function from Michael Somos, Mar 31 2005
A291755(n) = (1/2)*(2 + ((A002326(n)+eulerphi(n+n+1))^2) - A002326(n) - 3*eulerphi(n+n+1));

Scheme

(define (A291755 n) (* 1/2 (+ (expt (+ (A002326 n) (A000010 (+ 1 n n))) 2) (- (A002326 n)) (- (* 3 (A000010 (+ 1 n n)))) 2)))

Formula

a(n) = (1/2)*(2 + ((A002326(n) + A000010(2n+1))^2) - A002326(n) - 3*A000010(2n+1)).