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Search: id:A003557
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| A003557 |
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n divided by largest square-free divisor of n. |
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+0
27
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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; listen)
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OFFSET
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1,4
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COMMENT
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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
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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
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Multiplicative with a(p^e) = p^(e-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 23 2001
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MAPLE
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Contribution from Peter Luschny (peter(AT)luschny.de), Jun 29 2009: (Start)
A003557 := proc(n) local A, p, i, j, h, q;
A := [seq(j, j=1..n)]; p := 2;
while p <= n do for j from p by p to n do
if irem(A[j], p, 'q') = 0 then A[j] := q fi od;
p := nextprime(p) od; A end:
(End)
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MATHEMATICA
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Prepend[ Array[ #/Times@@(First[ Transpose[ FactorInteger[ # ] ] ])&, 100, 2 ], 1 ]
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CROSSREFS
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Cf. A007947, A062378, A062379.
Sequence in context: A104445 A000189 A000190 this_sequence A073752 A128708 A087653
Adjacent sequences: A003554 A003555 A003556 this_sequence A003558 A003559 A003560
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Marc LeBrun (mlb(AT)well.com)
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EXTENSIONS
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Program added Apr 10, 1997 (og).
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