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

120, 168, 240, 264, 280, 312, 336, 360, 408, 420, 440, 456, 480, 504, 520, 528, 552, 560, 600, 616, 624, 660, 672, 680, 696, 720, 728, 744, 760, 780, 792, 816, 880, 888, 912, 920, 924, 936, 952, 960, 984, 1008, 1020, 1032, 1040, 1056, 1064, 1080, 1092, 1104, 1120, 1128, 1140, 1144, 1155, 1160, 1176, 1200

Offset

1,1

Comments

Numbers n such that A046072(n) = 4.

Links

Table of n, a(n) for n=1..58.

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[1200], A046072[#] == 4&] (* Jean-François Alcover, Dec 22 2021, after Geoffrey Critzer in A046072 *)

Prog

(PARI) for(n=1, 3*10^3, my(t=#(znstar(n)[2])); if(t==4, print1(n, ", ")));

Crossrefs

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).

Sequence in context: A099832 A111399 A030634 * A377156 A189975 A232461

Adjacent sequences: A272591 A272592 A272593 * A272595 A272596 A272597

Keyword

nonn

Author

Joerg Arndt, May 05 2016

Status

approved