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

%I A272598 #13 Dec 22 2021 11:44:46
%S A272598 2042040,2282280,2762760,2984520,3483480,3527160,3612840,3723720,
%T A272598 4037880,4084080,4269720,4444440,4555320,4564560,4772040,4869480,
%U A272598 4924920,5091240,5165160,5383560,5442360,5525520,5542680,5645640,5754840,5811960,5969040,6016920,6126120,6163080,6240360,6366360,6431880,6440280
%N A272598 Numbers n such that the multiplicative group modulo n is the direct product of 8 cyclic groups.
%C A272598 Numbers n such that A046072(n) = 8.
%t A272598 A046072[n_] := Which[n == 1 || n == 2, 1,
%t A272598      OddQ[n], PrimeNu[n],
%t A272598      EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t A272598      Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
%t A272598      Divisible[n, 8], PrimeNu[n] + 1];
%t A272598 Select[Range[120, 120*10^5, 120], A046072[#] == 8&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o A272598 (PARI) for(n=1, 10^7, my(t=#(znstar(n)[2])); if(t==8, print1(n, ", ")));
%Y A272598 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).
%K A272598 nonn
%O A272598 1,1
%A A272598 _Joerg Arndt_, May 05 2016