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A272599 Numbers n such that the multiplicative group modulo n is the direct product of 9 cyclic groups.

%I A272599 #14 Dec 22 2021 11:44:38
%S A272599 38798760,46966920,52492440,59219160,63303240,66186120,68643960,
%T A272599 70750680,75555480,77597520,80120040,81124680,83723640,84444360,
%U A272599 85645560,86551080,87807720,92520120,93573480,93933840,95975880,98138040,102222120,102287640,104772360,104984880,107267160,107987880,108228120,109341960,110427240
%N A272599 Numbers n such that the multiplicative group modulo n is the direct product of 9 cyclic groups.
%C A272599 Numbers n such that A046072(n) = 9.
%t A272599 A046072[n_] := Which[n == 1 || n == 2, 1,
%t A272599      OddQ[n], PrimeNu[n],
%t A272599      EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t A272599      Divisible[n, 4] && ! Divisible[n, 8], PrimeNu[n],
%t A272599      Divisible[n, 8], PrimeNu[n] + 1];
%t A272599 Select[Range[840, 840*140000, 840], A046072[#] == 9&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o A272599 (PARI) for(n=1, 10^9, my(t=#(znstar(n)[2])); if(t==9, print1(n, ", ")));
%Y A272599 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), A272598 (k=8).
%K A272599 nonn
%O A272599 1,1
%A A272599 _Joerg Arndt_, May 05 2016