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

2,1

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.

Links

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

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.]

Example

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,
...

Prog

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

Crossrefs

Inverse: A253562.

The leftmost column: A000079. Topmost row: A253568.

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

Sequence in context: A035312 A056230 A285321 * A354960 A373623 A119919

Adjacent sequences: A253558 A253559 A253560 * A253562 A253563 A253564

Keyword

nonn,tabl

Author

Antti Karttunen, Jan 03 2015

Status

approved