A333992 a(n) is the multiplicative order of the n-th prime number q modulo (q-1)#.

1, 1, 2, 4, 6, 20, 60, 120, 144, 7920, 18480, 18480, 7920, 27720, 2520, 637560, 8288280, 480720240, 240360120, 480720240, 480720240, 480720240, 240360120, 9854764920, 19709529840, 9854764920, 16424608200, 670124014560, 88791431929200, 88791431929200

Offset

1,3

Links

Table of n, a(n) for n=1..30.

Mathoverflow, What is the multiplicative order of this number

Example

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

Maple

with(NumberTheory):
primorial := proc(n::integer)
local total := 1:
local count := 2;
for count from 2 to n do
if isprime(count) then
total *= count
endif;
end:
return total;
end proc:
numberOfTerms := 3;
List := [seq(MultiplicativeOrder(ithprime(i), primorial(ithprime[i]-1)), i=1..numberOfTerms)]

Mathematica

a[n_] := MultiplicativeOrder[Prime[n], Times @@ Prime[Range[n-1]]];
a /@ Range[30] (* Jean-François Alcover, Nov 03 2020 *)

Prog

(PARI) a(n)={znorder(Mod(prime(n), vecprod(primes(n-1))))} \\ Andrew Howroyd, Sep 05 2020

Crossrefs

Cf. A002110.

Sequence in context: A245766 A193774 A241210 * A176652 A251724 A326363

Adjacent sequences: A333989 A333990 A333991 * A333993 A333994 A333995

Keyword

nonn

Author

Yassine Lagrida, Sep 04 2020

Extensions

Terms a(16) and beyond from Andrew Howroyd, Sep 05 2020

Status

approved