cp's OEIS Frontend

A272592 Numbers n such that the multiplicative group modulo n is the direct product of 2 cyclic groups.

%I A272592 #20 Jan 09 2022 02:55:28
%S A272592 8,12,15,16,20,21,28,30,32,33,35,36,39,42,44,45,51,52,55,57,63,64,65,
%T A272592 66,68,69,70,75,76,77,78,85,87,90,91,92,93,95,99,100,102,108,110,111,
%U A272592 114,115,116,117,119,123,124,126,128,129,130,133,135,138,141,143,145,147,148,150,153,154,155,159,161
%N A272592 Numbers n such that the multiplicative group modulo n is the direct product of 2 cyclic groups.
%C A272592 Numbers n such that A046072(n) = 2.
%C A272592 Numbers are of the form p^e*q^f, 2*p^e*q^f, 4p^e, or 2^(e+2) where p and q are distinct odd primes and e,f >= 1. - _Charles R Greathouse IV_, Jan 09 2022
%t A272592 A046072[n_] := Which[n == 1 || n == 2, 1,
%t A272592      OddQ[n], PrimeNu[n],
%t A272592      EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
%t A272592      Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
%t A272592      Divisible[n, 8], PrimeNu[n] + 1];
%t A272592 Select[Range[200], A046072[#] == 2&] (* _Jean-François Alcover_, Dec 22 2021, after _Geoffrey Critzer_ in A046072 *)
%o A272592 (PARI) for(n=1,10^3, my(t=#(znstar(n)[2]));if(t==2,print1(n,", ")));
%Y A272592 Cf. A046072.
%Y A272592 Supersequence of A225375.
%Y A272592 Direct product of k groups: A033948 (k=1), A272593 (k=3), A272594 (k=4), A272595 (k=5), A272596 (k=6), A272597 (k=7), A272598 (k=8), A272599 (k=9).
%K A272592 nonn
%O A272592 1,1
%A A272592 _Joerg Arndt_, May 03 2016