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Search: id:A157928
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| A157928 |
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S(n)= index of prime factorization. |
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+0
1
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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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n) = 1 if n = Product p_i^k_i, otherwise a(n) = 0, for p = primes (A000040), k = natural numbers (A000027). a(0) = 0, a(1) = 0, a(n) = 1 for n >= 2. a(n) = A057427(n - 1) for n >= 2. a(n) for n >= 1 is Dirichlet convolution of following functions b(n), c(n), i.e. a(n) = Sum_{d|n} b(d)*c(n/d)): a(n) = A157658(n) * A000012(n), a(n) = A008683(n) * A032741(n). Examples of Dirichlet convolutions with function a(n), i.e. b(n) = Sum_{d|n} a(d)*c(n/d): a(n) * A000010(n) = A051953(n), a(n) * A000027(n) = A001065(n), a(n) * A000012(n) = A032741(n).
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CROSSREFS
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Cf. A000040, A000027, A057427, A157658, A000012, A008683, A032741, A000010, A051953, A001065.
Sequence in context: A152228 A086823 A104121 this_sequence A159075 A063524 A084928
Adjacent sequences: A157925 A157926 A157927 this_sequence A157929 A157930 A157931
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KEYWORD
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nonn,uned
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AUTHOR
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Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 09 2009
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