A325309 Square array read by downward antidiagonals: A(n, k) is the k-th Niven number (or Harshad number) in base n.

1, 2, 1, 4, 2, 1, 6, 3, 2, 1, 8, 4, 3, 2, 1, 10, 6, 4, 3, 2, 1, 12, 8, 6, 4, 3, 2, 1, 16, 9, 8, 5, 4, 3, 2, 1, 18, 10, 9, 6, 5, 4, 3, 2, 1, 20, 12, 12, 8, 6, 5, 4, 3, 2, 1, 21, 15, 16, 10, 10, 6, 5, 4, 3, 2, 1, 24, 16, 18, 12, 12, 7, 6, 5, 4, 3, 2, 1, 32, 18, 20, 15, 15, 8, 7, 6, 5, 4, 3, 2, 1

Offset

2,2

Links

Paolo Xausa, Table of n, a(n) for n = 2..11326 (first 150 antidiagonals, flattened).

Eric Weisstein's World of Mathematics, Harshad Number.

Wikipedia, Harshad number.

Example

The array starts as follows:
  1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 21, 24, 32, 34, 36, 40, 42, 48, 55, 60, ...
  1, 2, 3, 4, 6,  8,  9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, ...
  1, 2, 3, 4, 6,  8,  9, 12, 16, 18, 20, 21, 24, 28, 30, 32, 33, 35, 36, 40, ...
  1, 2, 3, 4, 5,  6,  8, 10, 12, 15, 16, 18, 20, 24, 25, 26, 27, 28, 30, 32, ...
  1, 2, 3, 4, 5,  6, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 42, 44, 45, 48, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 12, 14, 15, 16, 18, 21, 24, 27, 28, 30, 32, ...
  1, 2, 3, 4, 5,  6,  7,  8, 14, 16, 21, 24, 28, 32, 35, 40, 42, 48, 49, 56, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 35, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 22, 24, 33, 36, 44, 48, 55, 60, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 18, 24, 26, 27, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 26, 28, 39, 42, 52, 56, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 21, 28, 30, 32, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 30, 32, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, ...
  1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 34, 36, ...
  ...

Mathematica

A325309list[d_] := Module[{a, m}, a = Table[m = 0; Table[While[!Divisible[++m, DigitSum[m, n]]]; m, d+2-n], {n, d+1, 2, -1}]; Array[Reverse[Diagonal[a, #-d]] &, d]]; (* Generates d antidiagonals *)
A325309list[15] (* Paolo Xausa, May 03 2026 *)

Prog

(PARI) row(n, terms) = my(i=0); for(x=1, oo, if(i >= terms, break); if(x%sumdigits(x, n)==0, print1(x, ", "); i++))
array(rows, cols) = for(x=2, rows+1, row(x, cols); print(""))
array(18, 20) \\ Print initial 18 rows and 20 columns of array

Crossrefs

Cf. A049445 (row 2), A064150 (row 3), A064438 (row 4), A064481 (row 5), A395676 (row 6), A395677 (row 7), A245802 (row 8), A395678 (row 9), A005349 (row 10).

Cf. A005349.

Sequence in context: A347069 A378308 A365901 * A211956 A128177 A087738

Adjacent sequences: A325306 A325307 A325308 * A325310 A325311 A325312

Keyword

nonn,tabl,base,easy

Author

Felix Fröhlich, Sep 06 2019

Status

approved