OFFSET
1,6
COMMENTS
For squarefree n this gives the total number of groups of order n.
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 1..10000
M. Ram Murty and V. Kumar Murty, On groups of squarefree order, Math. Ann. 267, no. 3, 299-309, 1984.
FORMULA
PROG
(Sage)
def pnu(pp, m) : return prod(gcd(pp, q-1) for q in prime_divisors(m))
def a(n) : s = n.radical(); return sum(prod(sum((pnu(p^(k+1), s//prod(c)) - pnu(p^k, s//prod(c))) // (p^k*(p-1)) for k in range(n.valuation(p))) for p in c) for c in powerset(prime_divisors(n)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Sep 15 2014
STATUS
approved