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A272597 Numbers n such that the multiplicative group modulo n is the direct product of 7 cyclic groups.

%I A272597 #13 Dec 22 2021 11:44:51
%S A272597 120120,157080,175560,185640,207480,212520,240240,251160,267960,
%T A272597 271320,286440,291720,314160,316680,326040,328440,338520,341880,
%U A272597 351120,360360,367080,371280,378840,394680,397320,404040,408408,414120,414960,425040,426360,434280,442680,447720,456456,462840,469560,471240
%N A272597 Numbers n such that the multiplicative group modulo n is the direct product of 7 cyclic groups.
%C A272597 Numbers n such that A046072(n) = 7.
%t A272597 A046072[n_] := Which[n == 1 || n == 2, 1,
%t A272597      OddQ[n], PrimeNu[n],
%t A272597      EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t A272597      Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
%t A272597      Divisible[n, 8], PrimeNu[n] + 1];
%t A272597 Select[Range[5*10^5], A046072[#] == 7&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o A272597 (PARI) for(n=1, 10^6, my(t=#(znstar(n)[2])); if(t==7, print1(n, ", ")));
%Y A272597 Direct product of k groups: A033948 (k=1), A272592 (k=2), A272593 (k=3), A272594 (k=4), A272595 (k=5), A272596 (k=6), A272598 (k=8), A272599 (k=9).
%K A272597 nonn
%O A272597 1,1
%A A272597 _Joerg Arndt_, May 05 2016