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A068494 a(n) = n mod phi(n). 9
0, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 7, 0, 1, 0, 1, 4, 9, 2, 1, 0, 5, 2, 9, 4, 1, 6, 1, 0, 13, 2, 11, 0, 1, 2, 15, 8, 1, 6, 1, 4, 21, 2, 1, 0, 7, 10, 19, 4, 1, 0, 15, 8, 21, 2, 1, 12, 1, 2, 27, 0, 17, 6, 1, 4, 25, 22, 1, 0, 1, 2, 35, 4, 17, 6, 1, 16, 27, 2, 1, 12, 21, 2, 31, 8, 1, 18, 19, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

By Lehmer's Conjecture, when n > 2 then a(n) = 1 if and only if n is prime. The Notices article states "Lehmer's Conjecture (1932). phi(n) | (n-1) if and only if n is prime." - Michael Somos, Oct 14 2011

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

D. H. Bailey and J. M. Borwein, Exploratory Experimentation and Computation, Notices of A. M. S. 58 (2011) 1410-1419, see p. 1416.

FORMULA

b^(n - a(n)) == 1 (mod n) for every b coprime to n. - Thomas Ordowski, Jun 30 2017

MATHEMATICA

Table[Mod[n, EulerPhi[n]], {n, 100}] (* Alonso del Arte, Feb 15 2013 *)

PROG

(PARI) for(n=1, 150, print1(n%eulerphi(n), ", "))

(PARI) {a(n) = n % eulerphi(n)}; /* Michael Somos, Oct 14 2011 */

(Haskell)

a068494 n = mod n $ a000010 n  -- Reinhard Zumkeller, Oct 14 2011

(MAGMA) [n mod EulerPhi(n): n in [1..100]]; // Vincenzo Librandi, Jul 19 2015

CROSSREFS

Sequence in context: A023445 A291760 A291759 * A200726 A195040 A250486

Adjacent sequences:  A068491 A068492 A068493 * A068495 A068496 A068497

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Mar 11 2002

STATUS

approved

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Last modified October 14 16:29 EDT 2019. Contains 328022 sequences. (Running on oeis4.)