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Search: id:A074587
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| A074587 |
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Sum of the coefficients of the n-th Moebius polynomial, M(n,x), where M(n,-1) = mu(n), the Moebius function of n. |
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+0
9
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| 1, 3, 7, 18, 37, 85, 171, 364, 736, 1513, 3027, 6168, 12337, 24849, 49743, 99872, 199745, 400322, 800645, 1602862, 3205903, 6414837, 12829675, 25665996, 51332030, 102676401, 205353546, 410732134, 821464269, 1642979927, 3285959855
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It seems that a(n+1)>2*a(n). - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 26 2002
a(n+1)=2*a(n)+1 if and only if n+1 is prime. - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 04 2002
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..300
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FORMULA
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a(n) = M(n, 1) (see A074586 for definition of M(n, x)). a(n) mod 2 = A008966(n). a(n) is asymptotic to c*2^n with c=1.530191414016549187154362361492633020259512374111... Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 04 2002
a(1)=1 a(n)=1+sum(i=1, n-1, floor(n/i)*a(i)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 04 2002
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EXAMPLE
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a(5) = M(5,1) = 1+9+15+10+2 = 37, since M(5,x) = 1 + 9x +15x^2 +10x^3 + 2x^4.
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MATHEMATICA
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m[n_, x_] := m[n, x]=1+x*Sum[m[i, x]Floor[n/i], {i, 1, n-1}]; Table[m[n, 1], {n, 1, 40}]
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CROSSREFS
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Cf. A074586.
Sequence in context: A069143 A097007 A006124 this_sequence A076700 A026533 A131630
Adjacent sequences: A074584 A074585 A074586 this_sequence A074588 A074589 A074590
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2002
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