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A157928
a(n) = 0 if n < 2, = 1 otherwise.
5
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
OFFSET
0,1
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
Decimal expansion of 1/900. - Elmo R. Oliveira, May 05 2024
FORMULA
a(n) = A057427(n-1) for n >= 2.
From Elmo R. Oliveira, Jul 20 2024: (Start)
G.f.: x^2/(1-x).
E.g.f.: exp(x) - x - 1. (End)
MATHEMATICA
PadRight[{0, 0}, 120, {1}] (* Harvey P. Dale, Jun 03 2019 *)
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Mar 09 2009
EXTENSIONS
Definition simplified by R. J. Mathar, May 17 2010
STATUS
approved