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.

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

Links

T. D. Noe, Table of n, a(n) for n=1..300

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

Adjacent sequences: A074584 A074585 A074586 * A074588 A074589 A074590

Keyword

easy,nice,nonn

Author

Paul D. Hanna, Aug 25 2002

Extensions

Cross reference corrected by Mats Granvik, Apr 23 2010

Status

approved