A253561 Square array read by antidiagonals: A(row,col) = A122111(A246278(row,col)).

2, 3, 4, 6, 9, 8, 5, 18, 27, 16, 12, 25, 54, 81, 32, 10, 36, 125, 162, 243, 64, 24, 50, 108, 625, 486, 729, 128, 7, 72, 250, 324, 3125, 1458, 2187, 256, 15, 49, 216, 1250, 972, 15625, 4374, 6561, 512, 20, 75, 343, 648, 6250, 2916, 78125, 13122, 19683, 1024, 48, 100, 375, 2401, 1944, 31250, 8748, 390625, 39366, 59049, 2048, 14, 144, 500, 1875, 16807, 5832, 156250, 26244, 1953125, 118098, 177147, 4096

Offset: 2

Author

Antti Karttunen, Jan 03 2015

Keywords

• nonn
• tabl

Comments

If we assume here that a(1) = 1 (but which is not explicitly included because outside of the array), then A253562 gives the inverse permutation.

The top row A253568 contains the same terms as A102750, but in different order.

Examples

			The top left corner of the array:
   2,  3,   6,   5,   12,   10,   24,    7,   15,   20,  48,   14,  96,   40,
   4,  9,  18,  25,   36,   50,   72,   49,   75,  100, 144,   98, 288,  200,
   8, 27,  54, 125,  108,  250,  216,  343,  375,  500, 432,  686, 864, 1000,
  16, 81, 162, 625,  324, 1250,  648, 2401, 1875, 2500,1296, 4802,2592, 5000,
  32,243, 486,3125,  972, 6250, 1944,16807, 9375,12500,3888,33614,7776,25000,
...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 2..466; the first 30 antidiagonals of the array

Crossrefs

Inverse: A253562.

The leftmost column: A000079. Topmost row: A253568.

Cf. A071178, A122111, A246278, A102750, A253560, A253563.

Programs

Scheme

(define (A253561 n) (A122111 (A246278 n)))

Formula

a(n) = A122111(A246278(n)). [As a linear sequence].

Other identities.

A071178(A(row,col)) = row for all col. [All terms on row k have k as the exponent of their largest prime factor.]

A253560(A(row,col)) = A(row+1,col). [For any n >= 2, A253560(n) gives the term which is immediately below n in the same column of this array.]