A272598 Numbers n such that the multiplicative group modulo n is the direct product of 8 cyclic groups.

2042040, 2282280, 2762760, 2984520, 3483480, 3527160, 3612840, 3723720, 4037880, 4084080, 4269720, 4444440, 4555320, 4564560, 4772040, 4869480, 4924920, 5091240, 5165160, 5383560, 5442360, 5525520, 5542680, 5645640, 5754840, 5811960, 5969040, 6016920, 6126120, 6163080, 6240360, 6366360, 6431880, 6440280

Offset

1,1

Comments

Numbers n such that A046072(n) = 8.

Links

Table of n, a(n) for n=1..34.

Mathematica

A046072[n_] := Which[n == 1 || n == 2, 1,
     OddQ[n], PrimeNu[n],
     EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
     Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
     Divisible[n, 8], PrimeNu[n] + 1];
Select[Range[120, 120*10^5, 120], A046072[#] == 8&] (* Jean-François Alcover, Dec 22 2021, after Geoffrey Critzer in A046072 *)

Prog

(PARI) for(n=1, 10^7, my(t=#(znstar(n)[2])); if(t==8, print1(n, ", ")));

Crossrefs

Direct product of k groups: A033948 (k=1), A272592 (k=2), A272593 (k=3), A272594 (k=4), A272595 (k=5), A272596 (k=6), A272597 (k=7), A272599 (k=9).

Sequence in context: A263892 A163682 A045871 * A190316 A034639 A206667

Adjacent sequences: A272595 A272596 A272597 * A272599 A272600 A272601

Keyword

nonn

Author

Joerg Arndt, May 05 2016

Status

approved