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A232105 Number of groups of order prime(n)^5. 4

%I #20 Nov 17 2017 01:04:40

%S 51,67,77,83,87,97,101,107,111,125,131,145,149,155,159,173,183,193,

%T 203,207,217,227,231,245,265,269,275,279,289,293,323,327,341,347,365,

%U 371,385,395,399,413,423,433,447,457,461,467,491,515,519,529,533,543,553

%N Number of groups of order prime(n)^5.

%H Eric M. Schmidt, <a href="/A232105/b232105.txt">Table of n, a(n) for n = 1..1000</a>

%H G. Bagnera, <a href="https://doi.org/10.1007/BF02419191">La composizione dei Gruppi finiti il cui grado e la quinta potenza di un numero primo</a>, Ann. Mat. Pura Appl. (3), 1 (1898), 137-228.

%H M. F. Newman, E. A. O'Brien and M. R. Vaughan-Lee, <a href="http://dx.doi.org/10.1016/j.jalgebra.2003.11.012">Groups and nilpotent Lie rings whose order is the sixth power of a prime</a>, J. Algebra, 278 (2004), 383-401.

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%F For a prime p > 3, the number of groups of order p^5 is 61 + 2p + 2 gcd(p - 1, 3) + gcd(p - 1, 4).

%o (Sage) def A232105(n) : p = nth_prime(n); return 51 if p==2 else 67 if p==3 else 61 + 2*p + 2*gcd(p - 1, 3) + gcd(p - 1, 4)

%o (GAP) A232105 := Concatenation([51, 67], List(Filtered([5..10^5], IsPrime), p -> 61 + 2 * p + 2 * Gcd(p-1, 3) + Gcd(p-1, 4))); # _Muniru A Asiru_, Nov 16 2017

%Y Cf. A000001, A000679, A090091, A090130, A090140, A232106, A232107.

%Y Cf. A050997.

%K nonn

%O 1,1

%A _Eric M. Schmidt_, Nov 21 2013

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Last modified March 28 13:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)