OFFSET
2,1
COMMENTS
Previous name was "Number of non-abelian groups of order prime(n)^6".
LINKS
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.
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 12 2016
STATUS
approved