A325309 - OEIS

%I #14 Sep 10 2019 21:49:29

%S 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,

%T 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,

%U 4,3,2,1,24,16,18,12,12,7,6,5,4,3,2,1,32,18

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Harshad_number">Harshad number</a>

%e The array starts as follows:

%e 1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 21, 24, 32, 34, 36, 40, 42, 48, 55, 60

%e 1, 2, 3, 4, 6,  8,  9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32

%e 1, 2, 3, 4, 6,  8,  9, 12, 16, 18, 20, 21, 24, 28, 30, 32, 33, 35, 36, 40

%e 1, 2, 3, 4, 5,  6,  8, 10, 12, 15, 16, 18, 20, 24, 25, 26, 27, 28, 30, 32

%e 1, 2, 3, 4, 5,  6, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 42, 44, 45, 48

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 12, 14, 15, 16, 18, 21, 24, 27, 28, 30, 32

%e 1, 2, 3, 4, 5,  6,  7,  8, 14, 16, 21, 24, 28, 32, 35, 40, 42, 48, 49, 56

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 35

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 22, 24, 33, 36, 44, 48, 55, 60

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 18, 24, 26, 27

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 26, 28, 39, 42, 52, 56

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 21, 28, 30, 32

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 30, 32

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24

%e 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 34, 36

%o (PARI) row(n, terms) = my(i=0); for(x=1, oo, if(i >= terms, break); if(x%sumdigits(x, n)==0, print1(x, ", "); i++))

%o array(rows, cols) = for(x=2, rows+1, row(x, cols); print(""))

%o array(18, 20) \\ Print initial 18 rows and 20 columns of array

%Y Cf. A049445 (row 2), A064150 (row 3), A064438 (row 4), A064481 (row 5), A245802 (row 8), A005349 (row 10).

%Y Cf. A005349.

%K nonn,tabl,base,easy

%O 2,2

%A _Felix Fröhlich_, Sep 06 2019