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 A232105 Number of groups of order prime(n)^5. 4
 51, 67, 77, 83, 87, 97, 101, 107, 111, 125, 131, 145, 149, 155, 159, 173, 183, 193, 203, 207, 217, 227, 231, 245, 265, 269, 275, 279, 289, 293, 323, 327, 341, 347, 365, 371, 385, 395, 399, 413, 423, 433, 447, 457, 461, 467, 491, 515, 519, 529, 533, 543, 553 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Eric M. Schmidt, Table of n, a(n) for n = 1..1000 G. Bagnera, La composizione dei Gruppi finiti il cui grado e la quinta potenza di un numero primo, Ann. Mat. Pura Appl. (3), 1 (1898), 137-228. M. F. Newman, E. A. O'Brien and M. R. Vaughan-Lee, Groups and nilpotent Lie rings whose order is the sixth power of a prime, J. Algebra, 278 (2004), 383-401. FORMULA 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). PROG (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) (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 CROSSREFS Cf. A000001, A000679, A090091, A090130, A090140, A232106, A232107. Cf. A050997. Sequence in context: A335346 A118147 A015863 * A225801 A242045 A113285 Adjacent sequences:  A232102 A232103 A232104 * A232106 A232107 A232108 KEYWORD nonn AUTHOR Eric M. Schmidt, Nov 21 2013 STATUS approved

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Last modified January 21 05:13 EST 2022. Contains 350473 sequences. (Running on oeis4.)