A272590 a(n) is the smallest number m such that the multiplicative group modulo m is the direct product of n cyclic groups.

2, 8, 24, 120, 840, 9240, 120120, 2042040, 38798760, 892371480, 25878772920, 802241960520, 29682952539240, 1217001054108840, 52331045326680120, 2459559130353965640, 130356633908760178920, 7691041400616850556280, 469153525437627883933080, 31433286204321068223516360

Offset: 1

Author

Joerg Arndt, May 05 2016

Keywords

• nonn

Comments

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

For n >= 2, positions of records of A046072. - Joerg Arndt, May 18 2018

Crossrefs

Cf. A002322, A102476, A058254.

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).

Programs

PARI

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

Formula

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

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

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