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

0,2

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

Links

Table of n, a(n) for n=0..59.

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

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.

Example

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.

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 *)

Crossrefs

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

Equals A006218(n+1) - 1.

Sequence in context: A277733 A288933 A129259 * A183873 A036386 A280417

Adjacent sequences: A077594 A077595 A077596 * A077598 A077599 A077600

Keyword

nonn

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Status

approved