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A157928
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a(n) = 0 if n < 2, = 1 otherwise.
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8
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0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| A characteristic function which indicates whether n has a prime factorization n = product p_i^e_i where p_i are primes (A000040) and e_i nonnegative exponents, at least one e_i nonzero.
a(n), n>=1, is also generated by the following Dirichlet convolutions:
a(n) = A157658(n) * A000012(n),
a(n) = A008683(n) * A032741(n).
a(n) appears as a factor in the following Dirichlet convolutions:
a(n) * A000010(n) = A051953(n),
a(n) * A000027(n) = A001065(n),
a(n) * A000012(n) = A032741(n).
a(n) is also both the number of disconnected 0-regular graphs on n vertices and the number of disconnected 1-regular graphs on 2n vertices. - Jason Kimberley, Sep 27 2011
Partial sums of A185012. - Jason Kimberley, Oct 15 2011
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LINKS
| J. S. Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g
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FORMULA
| a(n) = A057427(n - 1) for n >= 2.
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CROSSREFS
| Cf. A000040, A000027, A057427, A157658, A000012, A008683, A032741, A000010, A051953, A001065.
Sequence in context: A086823 A104121 A179770 * A159075 A178333 A063524
Adjacent sequences: A157925 A157926 A157927 * A157929 A157930 A157931
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KEYWORD
| nonn,easy
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AUTHOR
| Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 09 2009
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EXTENSIONS
| Definition simplified by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 17 2010
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