A280162 Number of subgroups of the group C_n x C_n x C_n x C_n, where C_n is the cyclic group of order n.

1, 67, 212, 1983, 1120, 14204, 3652, 43339, 24033, 75040, 19156, 420396, 35872, 244684, 237440, 821335, 99472, 1610211, 152404, 2220960, 774224, 1283452, 318532, 9187868, 810969, 2403424, 2222704, 7241916, 783904, 15908480, 1016836, 14445411, 4061072, 6664624, 4090240, 47657439, 2031712

Offset: 1

Author

Laszlo Toth, Dec 27 2016

Keywords

• nonn
• mult

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems
• G. A. Miller, On the subgroups of an abelian group, The Annals of Mathematics, 2nd Ser. 6:1 (1904), pp. 1-6.
• L. Toth, The number of subgroups of the group Z_m x Z_n x Z_r x Z_s, arXiv:1611.03302 [math.GR], (2016).

Crossrefs

Cf. A060724, A064803.

Programs

PARI

\\ For numsubgrp, see the Alekseyev link.
a(n)=my(f=factor(n)); prod(i=1,#f~, numsubgrp(f[i,1],f[i,2]*[1,1,1,1])) \\ Charles R Greathouse IV, Dec 27 2016

Extensions

Terms a(32) and beyond from Charles R Greathouse IV, Dec 27 2016