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A272595 Numbers n such that the multiplicative group modulo n is the direct product of 5 cyclic groups.

%I A272595 #14 Dec 22 2021 11:45:02
%S A272595 840,1320,1560,1680,1848,2040,2184,2280,2520,2640,2760,2856,3080,3120,
%T A272595 3192,3360,3432,3480,3640,3696,3720,3864,3960,4080,4200,4368,4440,
%U A272595 4488,4560,4620,4680,4760,4872,4920,5016,5040,5160,5208,5280,5304,5320,5460,5520,5544,5640,5712,5720,5880,5928,6072,6120
%N A272595 Numbers n such that the multiplicative group modulo n is the direct product of 5 cyclic groups.
%C A272595 Numbers n such that A046072(n) = 5.
%t A272595 A046072[n_] := Which[n == 1 || n == 2, 1,
%t A272595      OddQ[n], PrimeNu[n],
%t A272595      EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t A272595      Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
%t A272595      Divisible[n, 8], PrimeNu[n] + 1];
%t A272595 Select[Range[10^4], A046072[#] == 5&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o A272595 (PARI) for(n=1, 10^4, my(t=#(znstar(n)[2])); if(t==5, print1(n, ", ")));
%Y A272595 Direct product of k groups: A033948 (k=1), A272592 (k=2), A272593 (k=3), A272594 (k=4), A272596 (k=6), A272597 (k=7), A272598 (k=8), A272599 (k=9).
%K A272595 nonn
%O A272595 1,1
%A A272595 _Joerg Arndt_, May 05 2016