A077598 Coefficient of x^2 in the n-th Moebius polynomial (A074586), M(n,x), which satisfies M(n,-1)=mu(n) the Moebius function of n.

0, 0, 2, 8, 15, 30, 43, 67, 90, 123, 149, 203, 237, 290, 343, 415, 464, 556, 613, 716, 800, 899, 972, 1126, 1218, 1342, 1458, 1616, 1716, 1916, 2026, 2215, 2365, 2540, 2690, 2959, 3098, 3300, 3485, 3762, 3919, 4221, 4388, 4667, 4921, 5179, 5364, 5762

Offset

1,3

Comments

These terms seem to be asymptotic to c*n^2*log(n) with c=0.69...

Links

Table of n, a(n) for n=1..48.

Example

These are the coefficients of x^2 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

m[n_, 1] = 1; m[n_, k_] := m[n, k] = Sum[Floor[n/j]*m[j, k - 1], {j, 1, n - 1}]; a[n_] := m[n, 3]; Table[a[n], {n, 1, 48}] (* Jean-François Alcover, Jun 18 2013 *)

Crossrefs

Cf. A074586, A074587, A077596, A077597, A077599, A077600, A077601.

Sequence in context: A244476 A292202 A189952 * A095298 A297734 A100596

Adjacent sequences: A077595 A077596 A077597 * A077599 A077600 A077601

Keyword

nonn

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Status

approved