A271664 Erroneous version of A271811 (but for odd primes only).

491, 668, 844, 1183, 1474, 1961, 2293, 2936, 4190, 4686, 6244, 7363, 7999, 9266, 11456, 13835, 14766, 17449, 19348, 20419, 23578, 25781, 29375, 34549, 37228, 38644, 41471, 43018, 46001, 57454, 60913, 66371, 68263, 77960, 80016, 86254, 92689, 97076, 103946, 111005, 113496

Offset

2,1

Comments

Previous name was "Number of non-abelian groups of order prime(n)^6".

Links

Table of n, a(n) for n=2..42.

Rodney James, The groups of order p^6 (p an odd prime), Math. Comp. 34 (1980), 613-637.

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.

Index entries for sequences related to groups

Formula

a(n) = (13*p^2 + 145*p + 1338 + 80*gcd(p-1,3) + 45*gcd(p-1,4) + 8*gcd(p-1, 5) + 8*gcd(p-1,6))/4 for n>2 and where p = prime(n). See [Rodney James].

Prog

(PARI) a(n) = if (n==2, 491, my(p=prime(n)); (13*p^2 + 145*p + 1338 + 80*gcd(p-1, 3) + 45*gcd(p-1, 4) + 8*gcd(p-1, 5) + 8*gcd(p-1, 6))/4);

Crossrefs

Cf. A000001 (groups), A060689 (non-abelian groups),

Cf. A232106, A271664.

Cf. A030516 (primes^6)

Cf. A271811.

Sequence in context: A273809 A060975 A180457 * A082079 A260925 A217118

Adjacent sequences: A271661 A271662 A271663 * A271665 A271666 A271667

Keyword

nonn

Author

Michel Marcus, Apr 12 2016

Status

approved