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A074587
Sum of the coefficients of the n-th Moebius polynomial, M(n,x), where M(n,-1) = mu(n), the Moebius function of n.
10
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
OFFSET
1,2
COMMENTS
It seems that a(n+1)>2*a(n). - Benoit Cloitre, Aug 26 2002
a(n+1)=2*a(n)+1 if and only if n+1 is prime. - Benoit Cloitre, Dec 04 2002
FORMULA
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, Dec 04 2002
a(1)=1 a(n)=1+sum(i=1, n-1, floor(n/i)*a(i)). - Benoit Cloitre, Dec 04 2002
EXAMPLE
a(5) = M(5,1) = 1+9+15+10+2 = 37, since M(5,x) = 1 + 9x +15x^2 +10x^3 + 2x^4.
MATHEMATICA
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}]
CROSSREFS
Cf. A074586.
First column of A169659. [From Mats Granvik, Paul D. Hanna, Apr 05 2010]
Sequence in context: A011799 A006124 A197182 * A208715 A302408 A076700
KEYWORD
easy,nice,nonn
AUTHOR
Paul D. Hanna, Aug 25 2002
EXTENSIONS
Cross reference corrected by Mats Granvik, Apr 23 2010
STATUS
approved