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%I #17 Dec 22 2021 06:06:31
%S 24,40,48,56,60,72,80,84,88,96,104,105,112,132,136,140,144,152,156,
%T 160,165,176,180,184,192,195,200,204,208,210,216,220,224,228,231,232,
%U 248,252,255,260,272,273,276,285,288,296,300,304,308,315,320,328,330,340,344,345,348,352,357,364,368,372,376,380
%N Numbers n such that the multiplicative group modulo n is the direct product of 3 cyclic groups.
%C Numbers n such that A046072(n) = 3.
%t A046072[n_] := Which[n == 1 || n == 2, 1,
%t OddQ[n], PrimeNu[n],
%t EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
%t Divisible[n, 8], PrimeNu[n] + 1];
%t Select[Range[400], A046072[#] == 3&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o (PARI) for(n=1, 10^3, my(t=#(znstar(n)[2])); if(t==3, print1(n, ", ")));
%Y Cf. A046072.
%Y Direct product of k groups: A033948 (k=1), A272592 (k=2), A272594 (k=4), A272595 (k=5), A272596 (k=6), A272597 (k=7), A272598 (k=8), A272599 (k=9).
%K nonn
%O 1,1
%A _Joerg Arndt_, May 05 2016
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