A272040 a(n) = A000010(A000129(n)).

1, 1, 4, 4, 28, 24, 156, 128, 784, 1120, 5740, 2880, 33460, 37128, 150080, 147456, 1128256, 931392, 6446016, 4677120, 28514304, 44450560, 224075664, 106168320, 1265644800, 1560708240, 5970392064, 5588803584, 44560482148, 33497856000, 255263424000, 196368924672, 1210784762880

Offset

1,3

Comments

Luca and Stănică (2014) proved that a(n) is a power of 2 only for n = 1, 2, 3, 4 and 8. - Amiram Eldar, Jan 12 2026

Links

Amiram Eldar, Table of n, a(n) for n = 1..630

Florian Luca and Pantelimon Stănică, Equations with arithmetic functions of Pell numbers, Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 57 (105), No. 4 (2014), pp. 409-413; alternative link.

Example

a(3) = 4 because a(3) = A000010(A000129(3)) = A000010(5) = 4.

Mathematica

EulerPhi[LinearRecurrence[{2, 1}, {1, 2}, 33]] (* Amiram Eldar, Oct 21 2023 *)

Prog

(PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
a(n) = eulerphi(a000129(n));

Crossrefs

Cf. A000010, A000129, A000203, A065449, A363829, A363831, A363833, A364818.

Sequence in context: A066836 A227715 A173049 * A338672 A065237 A264586

Adjacent sequences: A272037 A272038 A272039 * A272041 A272042 A272043

Keyword

nonn

Author

Altug Alkan, May 06 2016

Status

approved