A332771 Positions of the Dirichlet inverse of the Euler totient function expansion of the partial sums of the Möbius inverse of the Harmonic numbers in the set of the sorted tuples that have upper and lower bounds -(k-1) and +(k-1).

1, 1, 3, 11, 197, 664, 25522, 283333

Offset

1,3

Comments

The sorting in the Mathematica program is lexicographic.

Links

Table of n, a(n) for n=1..8.

Formula

See program.

Example

M={{1}} where the last entry is {1}.
A={{1}} where the last entry {1} in M is found at position 1 in the ordered set of tuples A, therefore a(1)=1.
M={{1}, {2, -1}} where the last entry is {2,-1}.
A={{2, -1}, {2, 0}, {2, 1}} where the last entry {2,-1} in M is found at position 1 in the ordered set of tuples A, therefore a(2)=1.
M={{1}, {2, -1}, {3, 0, -2}} where the last entry is {3, 0, -2}.
A={{3, -1, -2}, {3, -1, -1}, {3, 0, -2}, {3, -1, 0}, {3, 0, -1}, {3, 1, -2}, {3, -1, 1}, {3, 0, 0}, {3, 1, -1}, {3, -1, 2}, {3, 0, 1}, {3, 1, 0}, {3, 0, 2}, {3, 1, 1}, {3, 1, 2}} where the last entry {3, 0, -2} in M is found at position 3 in the ordered set of tuples A, therefore a(3)=3.

Mathematica

Monitor[Flatten[Table[
   nnn = nnnn;
   g1 = Table[
     T = Tuples[
       Table[Table[If[k == 1, nn, n], {n, -(k - 1), k - 1}], {k, 1,
         nn}]];
     b = Sort[
       Table[{T[[n]], Total[T[[n]]/Range[Length[T[[n]]]]] - nn}, {n,
         1, Length[T]}], #1[[2]] < #2[[2]] &], {nn, 1, nnn}];
   A = Table[b[[n]][[1]], {n, 1, Length[b]}];
   Clear[T, n, k, b, a];
   nn = nnn;
   a[n_] := If[n < 1, 0, Sum[d MoebiusMu@d, {d, Divisors[n]}]];
   M = Table[
     Table[Sum[If[n >= k, a[GCD[n, k]], 0], {n, 1, m}], {k, 1,
       m}], {m, 1, nn}];
   Flatten[Position[A, M[[nnn]]]], {nnnn, 1, 8}]], nnnn]

Crossrefs

Sequence in context: A081484 A125738 A334176 * A092840 A007156 A289170

Adjacent sequences: A332768 A332769 A332770 * A332772 A332773 A332774

Keyword

nonn,more

Author

Mats Granvik, Feb 23 2020

Status

approved