# Mobius function times n approximately as eigenvalues

Aug 2nd, 2013
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1. (*Mathematica 8 program start*)
2. (*The Mobius function times "n" approximately as the eigenvalues of a matrix*)
3. Clear[nn, n, k, d, kolumn]
4. a[n_] := If[n < 1, 0, Sum[d MoebiusMu@d, {d, Divisors[n]}]]
5. Do[nn = j;
6. A3 = Range[nn]*0;
7. Do[kolumn = i;
8. A1 = Table[Table[a[GCD[n, k]], {k, 1, nn}], {n, 1, nn}];
9. MatrixForm[A1];
10. A1[[All, kolumn]];
11. MatrixForm[
12. Table[Table[
13. If[Mod[n, k] == 0, MoebiusMu[n/k]*A1[[All, kolumn]][[k]],
14. 0], {k, 1, nn}], {n, 1, nn}]];
15. a1 = Table[
16. Total[Table[
17. If[Mod[n, k] == 0, MoebiusMu[n/k]*A1[[All, kolumn]][[k]],
18. 0], {k, 1, nn}]], {n, 1, nn}];
19. a2 = Sign[a1]*Exp[Exp[Abs[a1]]];
20. A2 = Table[
21. Table[If[Mod[n, k] == 0, a2[[n/k]], 0], {k, 1, nn}], {n, 1, nn}];
22. MatrixForm[A2];
23. a3 = Table[
24. Total[Table[If[Mod[n, k] == 0, a2[[n/k]], 0], {k, 1, nn}]], {n,
25. 1, nn}];
26. A3[[i]] = a3;, {i, 1, nn}]
27. MatrixForm[A3];
28. (*Print[N[Log[Log[-Min[Eigenvalues[A3]]]],12]]*)
29. Print[N[Sign[Eigenvalues[A3]] Log[Log[Abs[Eigenvalues[A3]]]],
30. 12]], {j, 1, 13}]
31. (*program end*)