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A003557
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n divided by largest squarefree divisor of n.
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35
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1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 9, 2, 1, 1, 1, 16, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 8, 7, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, 1, 1, 3, 32, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 5, 2, 1, 1, 1, 8, 27, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 16, 1, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) is the size of the Frattini subgroup of the cyclic group C_n - Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 07 2001. Also of the Frattini subgroup of the dihedral group with 2*n elements. - Sharon Sela (sharonsela(AT)hotmail.com), Jan 01 2002
Number of solutions to x^m==0 (mod n) provided that n < 2^(m+1), i.e. the sequence of sequences A000188, A000189, A000190, etc. converges to this sequence. - Henry Bottomley (se16(AT)btinternet.com), Sep 18 2001
a(n) is the number of nilpotent elements in the ring Z/nZ. - Laszlo Toth (ltoth(AT)ttk.pte.hu), May 22 2009
The sequence of partial products of a(n) is A085056(n). [From Peter Luschny (peter(AT)luschny.de), Jun 29 2009]
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000
H. Bottomley, Some Smarandache-type multiplicative sequences
S. R. Finch, Idempotents and Nilpotents Modulo n (arXiv:math.NT/0605019)
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FORMULA
| Multiplicative with a(p^e) = p^(e-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 23 2001
a(n) = n/rad(n) = n/A007947(n) = sqrt(J_2(n)/J_2(rad(n))), where J_2(n) is A007434 [From Enrique Perez Herrero (psychgeometry(AT)gmail.com), Aug 31 2010]
a(n)=(J_k(n)/J_k(rad(n)))^(1/k), where J_k is the k-th Jordan Totient Function: (J_2 is A007434 and J_3 A059376). - Enrique Perez Herrero (psychgeometry(AT)gmail.com), Sep 03 2010
Dirichlet convolution of A000027 and A097945. - R. J. Mathar, Dec 20 2011
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MAPLE
| A003557 := n -> n/ilcm(op(numtheory[factorset](n))):
seq(A003557(n), n=1..98); # - Peter Luschny, Mar 23 2011.
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MATHEMATICA
| Prepend[ Array[ #/Times@@(First[ Transpose[ FactorInteger[ # ] ] ])&, 100, 2 ], 1 ]
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PROG
| (Sage)
def A003557(n) :
p = 1
for a in factor(n) :
if a[1] > 1 :
p = p * a[0]^(a[1]-1)
return p
[A003557(n) for n in (1..98)] # Peter Luschny, Feb 07 2012
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CROSSREFS
| Cf. A007947, A062378, A062379.
Sequence in context: A104445 A000189 A000190 * A073752 A128708 A087653
Adjacent sequences: A003554 A003555 A003556 * A003558 A003559 A003560
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KEYWORD
| nonn,easy,mult,changed
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AUTHOR
| Marc LeBrun (mlb(AT)well.com)
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EXTENSIONS
| Program added Apr 10, 1997 (og).
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