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Search: id:A068074
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| A068074 |
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a(n)=sum(d|n,(-1)^d*2^omega(n/d)) where omega(x) is the number of distinct prime factors in x factorization. |
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+0
1
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| -1, -1, -3, 1, -3, -3, -3, 3, -5, -3, -3, 3, -3, -3, -9, 5, -3, -5, -3, 3, -9, -3, -3, 9, -5, -3, -7, 3, -3, -9, -3, 7, -9, -3, -9, 5, -3, -3, -9, 9, -3, -9, -3, 3, -15, -3, -3, 15, -5, -5, -9, 3, -3, -7, -9, 9, -9, -3, -3, 9, -3, -3, -15, 9, -9, -9, -3, 3, -9, -9, -3, 15, -3, -3, -15, 3, -9, -9, -3, 15, -9, -3, -3, 9, -9, -3, -9, 9, -3
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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G. Tenenbaum and Jie Wu, Cours specialies No. 2: "Exercices corriges de theorie analytique et probabiliste des nombres", Collection SMF, chap. II.7.1, p. 105.
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FORMULA
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Asymptotic formula : sum(k=1, n, a(k)/k)=-C*ln(n)^2 with C=3*ln(2)/Pi^2
a(n) = -tau(n^2) for odd n and 2*tau(n^2/4)-tau(n^2) for even n. b(n) = abs(a(n)) is multiplicative with b(2^e) = abs(2*e-3) and b(p^e) = 2*e+1 for an odd prime p. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 25 2002
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CROSSREFS
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Cf. A048691.
Sequence in context: A059789 A023136 A152774 this_sequence A063195 A025796 A024163
Adjacent sequences: A068071 A068072 A068073 this_sequence A068075 A068076 A068077
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KEYWORD
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easy,nice,sign
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 14 2002
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