A273784 Frequency of the largest spectral component of the Moebius function of the first n numbers, for n>0. In case of a tie, use the smallest frequency.

1, 2, 2, 2, 3, 2, 4, 4, 5, 3, 6, 7, 7, 8, 8, 9, 9, 5, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 7, 18, 18, 19, 7, 20, 7, 21, 8, 8, 8, 8, 8, 24, 9, 25, 9, 26, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 32, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14

Offset: 1

Author

Andres Cicuttin, May 30 2016

Keywords

• nonn

Comments

The Discrete Fourier transform is applied to the list of Moebius function of first n numbers, then it is selected the position of the largest absolute value of the components of the transformed list. If there are several identical maxima then it is taken the lowest position of them.

A curious pattern (see link) shows that frequencies of most maximum spectral components are aligned along few convergent directions.

Examples

			For the first 60 numbers starting from 1, the absolute values of the discrete Fourier transform of the Moebius function of these numbers have a maximum at position 11, then a(60) = 11.
		

Links

• Andres Cicuttin, Scatter plot of first 20000 elements

Programs

Mathematica

Table[Position[b=Abs@Fourier@Table[MoebiusMu[j],{j,1,n}],Max[b]][[1,1]],{n,1,120}]