cp's OEIS Frontend

A272593 Numbers n such that the multiplicative group modulo n is the direct product of 3 cyclic groups.

%I A272593 #17 Dec 22 2021 06:06:31
%S A272593 24,40,48,56,60,72,80,84,88,96,104,105,112,132,136,140,144,152,156,
%T A272593 160,165,176,180,184,192,195,200,204,208,210,216,220,224,228,231,232,
%U A272593 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 A272593 Numbers n such that the multiplicative group modulo n is the direct product of 3 cyclic groups.
%C A272593 Numbers n such that A046072(n) = 3.
%t A272593 A046072[n_] := Which[n == 1 || n == 2, 1,
%t A272593      OddQ[n], PrimeNu[n],
%t A272593      EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t A272593      Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
%t A272593      Divisible[n, 8], PrimeNu[n] + 1];
%t A272593 Select[Range[400], A046072[#] == 3&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o A272593 (PARI) for(n=1, 10^3, my(t=#(znstar(n)[2])); if(t==3, print1(n, ", ")));
%Y A272593 Cf. A046072.
%Y A272593 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 A272593 nonn
%O A272593 1,1
%A A272593 _Joerg Arndt_, May 05 2016