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%I #12 Dec 07 2019 12:18:27
%S 1,1,1,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,3,2,2,1,2,1,2,1,2,1,4,1,1,1,2,
%T 1,2,1,2,2,3,1,6,1,2,1,2,1,2,1,2,1,3,1,2,2,2,2,2,1,6,1,2,2,1,1,4,1,3,
%U 1,4,1,2,1,2,1,2,1,6,1,3,1,2,1,6,1,2,1
%N Number of groups of order n for which all Sylow subgroups are cyclic.
%C For squarefree n this gives the total number of groups of order n.
%H Eric M. Schmidt, <a href="/A247371/b247371.txt">Table of n, a(n) for n = 1..10000</a>
%H M. Ram Murty and V. Kumar Murty, <a href="http://dx.doi.org/10.1007/BF01456092">On groups of squarefree order</a>, Math. Ann. 267, no. 3, 299-309, 1984.
%F a(A005117(n)) = A000001(A005117(n)). - _Michel Marcus_, Sep 15 2014
%o (Sage)
%o def pnu(pp, m) : return prod(gcd(pp, q-1) for q in prime_divisors(m))
%o 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)))
%Y Cf. A000001, A069209.
%K nonn
%O 1,6
%A _Eric M. Schmidt_, Sep 15 2014
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