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

8, 12, 15, 16, 20, 21, 28, 30, 32, 33, 35, 36, 39, 42, 44, 45, 51, 52, 55, 57, 63, 64, 65, 66, 68, 69, 70, 75, 76, 77, 78, 85, 87, 90, 91, 92, 93, 95, 99, 100, 102, 108, 110, 111, 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

Offset

1,1

Comments

Numbers n such that A046072(n) = 2.

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

Links

Table of n, a(n) for n=1..69.

Mathematica

A046072[n_] := Which[n == 1 || n == 2, 1,
     OddQ[n], PrimeNu[n],
     EvenQ[n] && !Divisible[n, 4], PrimeNu[n] - 1,
     Divisible[n, 4] && !Divisible[n, 8], PrimeNu[n],
     Divisible[n, 8], PrimeNu[n] + 1];
Select[Range[200], A046072[#] == 2&] (* Jean-François Alcover, Dec 22 2021, after Geoffrey Critzer in A046072 *)

Prog

(PARI) for(n=1, 10^3, my(t=#(znstar(n)[2])); if(t==2, print1(n, ", ")));

Crossrefs

Cf. A046072.

Supersequence of A225375.

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).

Sequence in context: A363863 A033949 A175594 * A062373 A180690 A194592

Adjacent sequences: A272589 A272590 A272591 * A272593 A272594 A272595

Keyword

nonn

Author

Joerg Arndt, May 03 2016

Status

approved