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A272596 Numbers n such that the multiplicative group modulo n is the direct product of 6 cyclic groups.

%I A272596 #14 Dec 22 2021 11:44:57
%S A272596 9240,10920,14280,15960,17160,18480,19320,21840,22440,24024,24360,
%T A272596 25080,26040,26520,27720,28560,29640,30360,31080,31416,31920,32760,
%U A272596 34320,34440,35112,35880,36120,36960,37128,38280,38640,38760,39480,40040,40920,41496,42504,42840,43680,44520,44880,45240,46200
%N A272596 Numbers n such that the multiplicative group modulo n is the direct product of 6 cyclic groups.
%C A272596 Numbers n such that A046072(n) = 6.
%t A272596 A046072[n_] := Which[n == 1 || n == 2, 1,
%t A272596      OddQ[n], PrimeNu[n],
%t A272596      EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t A272596      Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
%t A272596      Divisible[n, 8], PrimeNu[n] + 1];
%t A272596 Select[Range[5*10^4], A046072[#] == 6&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o A272596 (PARI) for(n=1, 10^5, my(t=#(znstar(n)[2])); if(t==6, print1(n, ", ")));
%Y A272596 Direct product of k groups: A033948 (k=1), A272592 (k=2), A272593 (k=3), A272594 (k=4), A272595 (k=5), A272597 (k=7), A272598 (k=8), A272599 (k=9).
%K A272596 nonn
%O A272596 1,1
%A A272596 _Joerg Arndt_, May 05 2016