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A144100 Numbers n such that n is strictly greater than f(n), where f(n) = 1 if n is prime, 2 * rad(n) if 4 divides n and rad(n) otherwise. 9
2, 3, 5, 7, 8, 9, 11, 13, 16, 17, 18, 19, 23, 24, 25, 27, 29, 31, 32, 36, 37, 40, 41, 43, 45, 47, 48, 49, 50, 53, 54, 56, 59, 61, 63, 64, 67, 71, 72, 73, 75, 79, 80, 81, 83, 88, 89, 90, 96, 97, 98, 99, 100, 101, 103, 104, 107, 108, 109, 112, 113, 117, 120, 121, 125, 126 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is the set of all integers n such that there exists a full period linear congruential pseudorandom number generator x -> bx + c (mod n), where b is not a multiple of n, b - 1 is a multiple of f(n) and c is a positive integer relatively prime to n.

4 is the only prime power not a member of the set: f(4) = 2 * rad(4) = 4.

This sequence consists of the primes and 2*A013929. - Charlie Neder, Jan 28 2019

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

A144907(a(n)) < a(n). - Reinhard Zumkeller, Mar 12 2014

EXAMPLE

2 is a member: f(2) = 1 and the sequence (0, 1, 0, ...) given by x -> x + 1 (mod 2) has period 2.

8 is a member: f(8) = 4 and the sequence (0, 1, 6, 7, 4, 5, 2, 3, 0, ...) given by x -> 5x + 1 (mod 8) has period 8.

18 is a member: f(18) = 6 and the sequence (0, 1, 14, 3, 4, 17, 6, 7, 2, 9, 10, 5, 12, 13, 8, 15, 16, 11, 0, ...) given by x -> 13x + 1 (mod 18) has period 18.

PROG

(PARI) rad(n) = local(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i]) ;

f(n) = if (isprime(n), 1, if ((n % 4)==0 , 2*rad(n), rad(n))); isok(n) = n > f(n); \\ Michel Marcus, Aug 09 2013

(Haskell)

a144100 n = a144100_list !! (n-1)

a144100_list = filter (\x -> a144907 x < x) [1..]

-- Reinhard Zumkeller, Mar 12 2014

CROSSREFS

Cf. A000040, A007947, A071139, A082377, A086486, A089352, A133810, A133811.

Sequence in context: A078643 A137698 A063743 * A328320 A086539 A171217

Adjacent sequences:  A144097 A144098 A144099 * A144101 A144102 A144103

KEYWORD

easy,nice,nonn

AUTHOR

Reikku Kulon, Sep 10 2008

STATUS

approved

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Last modified April 20 15:56 EDT 2021. Contains 343135 sequences. (Running on oeis4.)