A387657 Array read by ascending antidiagonals: A(n, k) = denominator(k^n/n), with k >= 0.

1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 3, 2, 1, 1, 5, 1, 1, 1, 1, 1, 6, 5, 4, 3, 2, 1, 1, 7, 3, 5, 1, 3, 1, 1, 1, 8, 7, 2, 5, 4, 1, 2, 1, 1, 9, 1, 7, 3, 1, 1, 3, 1, 1, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 11, 5, 1, 1, 7, 1, 5, 1, 1, 1, 1, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset

1,5

Links

Table of n, a(n) for n=1..91.

Example

Array of the fractions begins as:
  0/1, 1/1,  2/1,   3/1,    4/1,     5/1,    6/1, ...
  0/1, 1/2,  2/1,   9/2,    8/1,    25/2,   18/1, ...
  0/1, 1/3,  8/3,   9/1,   64/3,   125/3,   72/1, ...
  0/1, 1/4,  4/1,  81/4,   64/1,   625/4,  324/1, ...
  0/1, 1/5, 32/5, 243/5, 1024/5,   625/1, 7776/5, ...
  0/1, 1/6, 32/3, 243/2, 2048/3, 15625/6, 7776/1, ...
  ...

Mathematica

A[n_, k_]:=Denominator[k^n/n]; Table[A[n-k, k], {n, 13}, {k, 0, n-1}]//Flatten

Crossrefs

Cf. A000012 (k=0 or n=1) A000027 (diagonal and k=1,11,13), A004248, A112544, A387656 (numerator).

Columns give: A000012 (k=0), A000265 (k=2,4,8), A038502 (k=3,9), A132739 (k=5), A065330 (k=6,12), A242603 (k=7), A132740 (k=10).

Rows n=2..5 give: A000034, A169609, A010685, A171372.

Sequence in context: A239454 A108888 A124021 * A109626 A182285 A160182

Adjacent sequences: A387654 A387655 A387656 * A387658 A387659 A387660

Keyword

nonn,easy,frac,tabl

Author

Stefano Spezia, Sep 05 2025

Status

approved