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

%I #14 Dec 22 2021 11:44:38

%S 38798760,46966920,52492440,59219160,63303240,66186120,68643960,

%T 70750680,75555480,77597520,80120040,81124680,83723640,84444360,

%U 85645560,86551080,87807720,92520120,93573480,93933840,95975880,98138040,102222120,102287640,104772360,104984880,107267160,107987880,108228120,109341960,110427240

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

%C Numbers n such that A046072(n) = 9.

%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[840, 840*140000, 840], A046072[#] == 9&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)

%o (PARI) for(n=1, 10^9, my(t=#(znstar(n)[2])); if(t==9, print1(n, ", ")));

%Y 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 nonn

%O 1,1

%A _Joerg Arndt_, May 05 2016

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)