A077597 Coefficient of x in the n-th Moebius polynomial (A074586), M(n,x), which satisfies M(n,-1)=mu(n) the Moebius function of n.

0, 2, 4, 7, 9, 13, 15, 19, 22, 26, 28, 34, 36, 40, 44, 49, 51, 57, 59, 65, 69, 73, 75, 83, 86, 90, 94, 100, 102, 110, 112, 118, 122, 126, 130, 139, 141, 145, 149, 157, 159, 167, 169, 175, 181, 185, 187, 197, 200, 206, 210, 216, 218, 226, 230, 238, 242, 246, 248, 260

Offset: 0

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Keywords

• nonn

Comments

This is also the number of ways to misidentify a solar mode of degree l with modes of lower degree. See paper with Lou Lanzerotti (in preparation). - David J. Thomson, Oct 28 2010

Examples

			These are the coefficients of x in the Moebius polynomials, which begin: M(1,x) = 1; M(2,x) = 1 + 2x; M(3,x) = 1 + 4x + 2x^2; M(4,x) = 1 + 7x + 8x^2 + 2x^3; M(5,x) = 1 + 9x + 15x^2 + 10x^3 + 2x^4; M(6,x) = 1 + 13x + 30x^2 + 27x^3 + 12x^4 + 2x^5; M(7,x) = 1 + 15x + 43x^2 + 57x^3 + 39x^4 + 14x^5 + 2x^6; M(8,x) = 1 + 19x + 67x^2 + 108x^3 + 98x^4 + 53x^5 + 16x^6 + 2x^7.
		

Links

• R. K. Guy, Conway's prime producing machine, Math. Mag. 56 (1983), no. 1, 26-33 (see p. 33).

Crossrefs

Cf. A074586, A074587, A077596, A077598, A077599, A077600, A077601, A085683.

Equals A006218(n+1) - 1.

Programs

Mathematica

a[n_] := Sum[ Floor[(n+1)/k], {k, 1, n+1}] - 1; Table[a[n], {n, 0, 59}] (* Jean-François Alcover, Jun 18 2013 *)

Formula

a(n) = Sum_{k = 1..n} floor((n+1)/k). - N. J. A. Sloane, Oct 28 2008

Since a(n) = A006218(n+1) - 1, asymptotics and bounds may be obtained from that entry.