A291755 - OEIS

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

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OFFSET

0,2

LINKS

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

FORMULA

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

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 *)

PROG

(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)))

CROSSREFS

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

Cf. also A292249, A292268.

Cf. A037226, A053006.

Sequence in context: A000221 A018612 A036127 * A018639 A029475 A332657

Adjacent sequences: A291752 A291753 A291754 * A291756 A291757 A291758

KEYWORD

nonn,changed

AUTHOR

Antti Karttunen, Oct 02 2017

STATUS

approved