A272590 - OEIS

%I #12 May 18 2018 13:06:31

%S 2,8,24,120,840,9240,120120,2042040,38798760,892371480,25878772920,

%T 802241960520,29682952539240,1217001054108840,52331045326680120,

%U 2459559130353965640,130356633908760178920,7691041400616850556280,469153525437627883933080,31433286204321068223516360

%N a(n) is the smallest number m such that the multiplicative group modulo m is the direct product of n cyclic groups.

%C Arguably a(1)=3, as the multiplicative group mod 2 has only one element, hence its factorization is the empty product. - _Joerg Arndt_, May 18 2018

%C For n >= 2, positions of records of A046072. - _Joerg Arndt_, May 18 2018

%F a(1) = 2, a(n) = 4 * prod(k=1..n-1, prime(k) ) for n >= 2.

%F a(n) = A102476(n) for n >= 2.

%F A002322(a(n)) = A058254(n).

%o (PARI) a(n)=if(n==1,2,4*prod(k=1,n-1,prime(k)));

%Y Cf. A002322, A102476, A058254.

%Y Numbers n such that the multiplicative group modulo n is the direct product of k cyclic groups: A033948 (k=1), A272593 (k=2), A272593 (k=3), A272594 (k=4), A272595 (k=5), A272596 (k=6), A272597 (k=7), A272598 (k=8), A272599 (k=9).

%K nonn

%O 1,1

%A _Joerg Arndt_, May 05 2016