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A032450 Period of finite sequence g(n) related to Poulet's Conjecture. 1
1, 3, 2, 2, 3, 7, 6, 12, 4, 2, 3, 12, 4, 7, 6, 4, 7, 6, 12, 15, 8, 12, 28, 6, 12, 4, 7, 12, 4, 7, 6, 28, 12, 6, 12, 4, 7, 8, 15, 8, 15, 31, 30, 72, 24, 60, 16, 6, 12, 4, 7, 24, 60, 16, 31, 30, 72, 8, 15, 12, 28, 16, 31, 30, 72, 24, 60, 12, 28, 8, 15, 60, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Poulet's Conjecture states that for any integer n, the sequence f_0(n) = n, f_2k+1(n)=sigma(f_2k(n)), f_2k(n)=phi(f_2k-1(n)) (where sigma = A000203 and phi = A000010) is eventually periodic.

REFERENCES

P. Poulet, Nouvelles suites arithmétiques, Sphinx vol. 2 (1932) pp. 53-54.

LINKS

Table of n, a(n) for n=1..73.

Leon Alaoglu and Paul Erdős, A conjecture in elementary number theory, Bull. Amer. Math. Soc. 50 (1944), 881-882.

Sean A. Irvine, Java program (github)

FORMULA

g(1)=n; thereafter g(2k)=sigma(g(2k-1)), g(2k+1)=phi(g(2k)).

EXAMPLE

Poulet's sequence starting at 1 is 1->1->1->.. which contributes [1]. Starting at 2: 2->3->2->3->.. which contributes [3,2]. Starting at 3: 3->4->2->3->2->3... which contributes [2,3]. Starting at 4: 4->7->6->12->4->7->6->12.. which contributes  [7, 6, 12, 4]. - R. J. Mathar, May 08 2020

CROSSREFS

Cf. A000010, A000203, A001229, A036845, A095955, A096865.

Sequence in context: A334592 A248756 A059942 * A046460 A327661 A117643

Adjacent sequences:  A032447 A032448 A032449 * A032451 A032452 A032453

KEYWORD

nonn

AUTHOR

Ursula Gagelmann (gagelmann(AT)altavista.net), Apr 07 1998

EXTENSIONS

Revised definition and added formula from Ursula Gagelmann, Apr 07 1998 - N. J. A. Sloane, May 08 2020

Missing a(42)=31 inserted and more terms from Sean A. Irvine, Jun 21 2020

STATUS

approved

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)