A333992 - OEIS

%I #24 Nov 04 2020 05:58:13

%S 1,1,2,4,6,20,60,120,144,7920,18480,18480,7920,27720,2520,637560,

%T 8288280,480720240,240360120,480720240,480720240,480720240,240360120,

%U 9854764920,19709529840,9854764920,16424608200,670124014560,88791431929200,88791431929200

%N a(n) is the multiplicative order of the n-th prime number q modulo (q-1)#.

%H Mathoverflow, <a href="https://mathoverflow.net/questions/364413/what-is-the-multiplicative-order-of-this-number">What is the multiplicative order of this number</a>

%e For n = 2, q = prime(2) = 3, we have (q-1)#=2, then the multiplicative order of q modulo (q-1)# is 1.

%p with(NumberTheory):

%p primorial := proc(n::integer)

%p local total := 1:

%p local count := 2;

%p for count from 2 to n do

%p if isprime(count) then

%p total *= count

%p endif;

%p end:

%p return total;

%p end proc:

%p numberOfTerms := 3;

%p List := [seq(MultiplicativeOrder(ithprime(i), primorial(ithprime[i]-1)),i=1..numberOfTerms)]

%t a[n_] := MultiplicativeOrder[Prime[n], Times @@ Prime[Range[n-1]]];

%t a /@ Range[30] (* _Jean-François Alcover_, Nov 03 2020 *)

%o (PARI) a(n)={znorder(Mod(prime(n),vecprod(primes(n-1))))} \\ _Andrew Howroyd_, Sep 05 2020

%Y Cf. A002110.

%K nonn

%O 1,3

%A _Yassine Lagrida_, Sep 04 2020

%E Terms a(16) and beyond from _Andrew Howroyd_, Sep 05 2020