A074587 - OEIS

%I #14 Mar 31 2012 20:55:21

%S 1,3,7,18,37,85,171,364,736,1513,3027,6168,12337,24849,49743,99872,

%T 199745,400322,800645,1602862,3205903,6414837,12829675,25665996,

%U 51332030,102676401,205353546,410732134,821464269,1642979927,3285959855

%N Sum of the coefficients of the n-th Moebius polynomial, M(n,x), where M(n,-1) = mu(n), the Moebius function of n.

%C It seems that a(n+1)>2*a(n). - _Benoit Cloitre_, Aug 26 2002

%C a(n+1)=2*a(n)+1 if and only if n+1 is prime. - _Benoit Cloitre_, Dec 04 2002

%H T. D. Noe, <a href="/A074587/b074587.txt">Table of n, a(n) for n=1..300</a>

%F 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

%F a(1)=1 a(n)=1+sum(i=1, n-1, floor(n/i)*a(i)). - _Benoit Cloitre_, Dec 04 2002

%e a(5) = M(5,1) = 1+9+15+10+2 = 37, since M(5,x) = 1 + 9x +15x^2 +10x^3 + 2x^4.

%t 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}]

%Y Cf. A074586.

%Y First column of A169659. [From Mats Granvik, _Paul D. Hanna_, Apr 05 2010]

%K easy,nice,nonn

%O 1,2

%A _Paul D. Hanna_, Aug 25 2002

%E Cross reference corrected by _Mats Granvik_, Apr 23 2010