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

Author

Paul D. Hanna, Aug 25 2002

Keywords

• easy
• nice
• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A074586.

First column of A169659. [From Mats Granvik, Paul D. Hanna, Apr 05 2010]

Programs

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}]

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

Extensions

Cross reference corrected by Mats Granvik, Apr 23 2010