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A247371 Number of groups of order n for which all Sylow subgroups are cyclic. 2
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, 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, 1, 4, 1, 2, 1, 2, 1, 2, 1, 6, 1, 3, 1, 2, 1, 6, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
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

a(A005117(n)) = A000001(A005117(n)). - Michel Marcus, Sep 15 2014

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

Cf. A000001, A069209.

Sequence in context: A247462 A323172 A327403 * A331177 A173751 A126864

Adjacent sequences:  A247368 A247369 A247370 * A247372 A247373 A247374

KEYWORD

nonn

AUTHOR

Eric M. Schmidt, Sep 15 2014

STATUS

approved

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Last modified January 20 14:02 EST 2020. Contains 331094 sequences. (Running on oeis4.)