A152007 a(n) = (2^phi(3^n)-1)/3^n.

1, 1, 7, 9709, 222399981598543, 24057640120673299065081231814259802792690247621

Offset

0,3

Comments

The next term is too large to display.

With the exception of 7 there are no primes in this sequence.

All numbers in this sequence are squarefree.

a(n) is divisible by a(k) for every k < n.

The sequence of number of digits of a(n), n >= 1, is 1, 1, 1, 4, 15, 47, 144, 436, 1313, 3946, 11846, 35546, 106648, 319954, 959872, 2879628, 8638896, 25916701, 77750117, 233250368, 699751120,... - Wolfdieter Lang, Feb 21 2014

Each a(n) is by definition the same as the repetend of 1/3^n, viewed as a binary integer. E.g., 1/9 = .000111000111...; consequently a(2) = 000111 (base 2) = 7 (base 10) - Joe Slater, Nov 29 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..7

W. Lang, On Collatz' Words, Sequences and Trees, arXiv preprint arXiv:1404.2710 [math.NT], 2014  and J. Int. Seq. 17 (2014) # 14.11.7.

Formula

a(n) = (4^(3^(n-1)) - 1)/3^n for n>=1, a(0) = 1, with EulerPhi(1) = 1 = A000010(1). - Wolfdieter Lang, Feb 21 2014

Mathematica

Table[(2^EulerPhi[3^n] - 1)/3^n, {n, 0, 10}]

Prog

(Magma) [(2^EulerPhi(3^n)-1)/3^n: n in [0..6]]; // Vincenzo Librandi, Feb 23 2014
(PARI) a(n)=(2^eulerphi(3^n)-1)/3^n \\ Charles R Greathouse IV, Nov 29 2016

Crossrefs

Cf. A008776, A152008, A234039.

Sequence in context: A212937 A074489 A067248 * A350148 A242773 A333338

Adjacent sequences: A152004 A152005 A152006 * A152008 A152009 A152010

Keyword

nonn

Author

Artur Jasinski, Nov 19 2008

Extensions

Edited by N. J. A. Sloane, Nov 28 2008

Offset corrected from Wolfdieter Lang, Feb 21 2014

Definition clarified by Joerg Arndt, Feb 23 2014

Status

approved