cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A247371 Number of groups of order n for which all Sylow subgroups are cyclic.

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%I A247371 #12 Dec 07 2019 12:18:27
%S A247371 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 A247371 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 A247371 1,4,1,2,1,2,1,2,1,6,1,3,1,2,1,6,1,2,1
%N A247371 Number of groups of order n for which all Sylow subgroups are cyclic.
%C A247371 For squarefree n this gives the total number of groups of order n.
%H A247371 Eric M. Schmidt, <a href="/A247371/b247371.txt">Table of n, a(n) for n = 1..10000</a>
%H A247371 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 A247371 a(A005117(n)) = A000001(A005117(n)). - _Michel Marcus_, Sep 15 2014
%o A247371 (Sage)
%o A247371 def pnu(pp, m) : return prod(gcd(pp, q-1) for q in prime_divisors(m))
%o A247371 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 A247371 Cf. A000001, A069209.
%K A247371 nonn
%O A247371 1,6
%A A247371 _Eric M. Schmidt_, Sep 15 2014