A272597 Numbers n such that the multiplicative group modulo n is the direct product of 7 cyclic groups.

120120, 157080, 175560, 185640, 207480, 212520, 240240, 251160, 267960, 271320, 286440, 291720, 314160, 316680, 326040, 328440, 338520, 341880, 351120, 360360, 367080, 371280, 378840, 394680, 397320, 404040, 408408, 414120, 414960, 425040, 426360, 434280, 442680, 447720, 456456, 462840, 469560, 471240

Offset: 1

Author

Joerg Arndt, May 05 2016

Keywords

• nonn

Comments

Numbers n such that A046072(n) = 7.

Crossrefs

Direct product of k groups: A033948 (k=1), A272592 (k=2), A272593 (k=3), A272594 (k=4), A272595 (k=5), A272596 (k=6), A272598 (k=8), A272599 (k=9).

Programs

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[5*10^5], A046072[#] == 7&] (* Jean-François Alcover, Dec 22 2021, after Geoffrey Critzer in A046072 *)

PARI

for(n=1, 10^6, my(t=#(znstar(n)[2])); if(t==7, print1(n, ", ")));