A152007 - OEIS

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A152007

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

1, 1, 7, 9709, 222399981598543, 24057640120673299065081231814259802792690247621 (list; graph; refs; listen; history; text; internal format)

	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`

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Last modified February 6 01:28 EST 2023. Contains 360091 sequences. (Running on oeis4.)