cp's OEIS Frontend

A272594 Numbers n such that the multiplicative group modulo n is the direct product of 4 cyclic groups.

%I A272594 #16 Dec 22 2021 11:45:09
%S A272594 120,168,240,264,280,312,336,360,408,420,440,456,480,504,520,528,552,
%T A272594 560,600,616,624,660,672,680,696,720,728,744,760,780,792,816,880,888,
%U A272594 912,920,924,936,952,960,984,1008,1020,1032,1040,1056,1064,1080,1092,1104,1120,1128,1140,1144,1155,1160,1176,1200
%N A272594 Numbers n such that the multiplicative group modulo n is the direct product of 4 cyclic groups.
%C A272594 Numbers n such that A046072(n) = 4.
%t A272594 A046072[n_] := Which[n == 1 || n == 2, 1,
%t A272594      OddQ[n], PrimeNu[n],
%t A272594      EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t A272594      Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
%t A272594      Divisible[n, 8], PrimeNu[n] + 1];
%t A272594 Select[Range[1200], A046072[#] == 4&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o A272594 (PARI) for(n=1, 3*10^3, my(t=#(znstar(n)[2])); if(t==4, print1(n, ", ")));
%Y A272594 Direct product of k groups: A033948 (k=1), A272592 (k=2), A272593 (k=3), A272595 (k=5), A272596 (k=6), A272597 (k=7), A272598 (k=8), A272599 (k=9).
%K A272594 nonn
%O A272594 1,1
%A A272594 _Joerg Arndt_, May 05 2016