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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). 0
1, 1, 3, 11, 197, 664, 25522, 283333 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The sorting in the Mathematica program is lexicographic.
LINKS
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
KEYWORD
nonn,more
AUTHOR
Mats Granvik, Feb 23 2020
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)