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A272590
a(n) is the smallest number m such that the multiplicative group modulo m is the direct product of n cyclic groups.
1
2, 8, 24, 120, 840, 9240, 120120, 2042040, 38798760, 892371480, 25878772920, 802241960520, 29682952539240, 1217001054108840, 52331045326680120, 2459559130353965640, 130356633908760178920, 7691041400616850556280, 469153525437627883933080, 31433286204321068223516360
OFFSET
1,1
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
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).
PROG
(PARI) a(n)=if(n==1, 2, 4*prod(k=1, n-1, prime(k)));
CROSSREFS
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).
Sequence in context: A157005 A123775 A052624 * A361991 A087982 A176475
KEYWORD
nonn
AUTHOR
Joerg Arndt, May 05 2016
STATUS
approved