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

1, 1, 7, 9709, 222399981598543, 24057640120673299065081231814259802792690247621

Offset: 0

Author

Artur Jasinski, Nov 19 2008

Keywords

• nonn

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.

Crossrefs

Cf. A008776, A152008, A234039.

Programs

Magma

[(2^EulerPhi(3^n)-1)/3^n: n in [0..6]]; // Vincenzo Librandi, Feb 23 2014

Mathematica

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

PARI

a(n)=(2^eulerphi(3^n)-1)/3^n \\ Charles R Greathouse IV, Nov 29 2016

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

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