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A272594
Numbers n such that the multiplicative group modulo n is the direct product of 4 cyclic groups.
9
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.
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
KEYWORD
nonn
AUTHOR
Joerg Arndt, May 05 2016
STATUS
approved