A104245 Suppose n=(p1^e1)(p2^e2)... where p1,p2,... are the prime numbers and e1,e2,... are nonnegative integers. Then we can define Pn(x) = e1 + (e2)*x + (e3)*(x^2) + (e4)*(x^3) + ... + (ek)*(x^(k-1)) + ... The sequence is the table T(x,n)=Pn(x) read by antidiagonals.

0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 2, 1, 0, 1, 4, 2, 4, 2, 0, 1, 5, 2, 9, 3, 1, 0, 1, 6, 2, 16, 4, 8, 3, 0, 1, 7, 2, 25, 5, 27, 3, 2, 0, 1, 8, 2, 36, 6, 64, 3, 4, 2, 0, 1, 9, 2, 49, 7, 125, 3, 6, 5, 1, 0, 1, 10, 2, 64, 8, 216, 3, 8, 10, 16, 3, 0, 1, 11, 2, 81, 9, 343, 3, 10, 17, 81, 4, 1, 0, 1, 12, 2

Offset: 1

Author

Olaf Voß, Feb 26 2005

Keywords

• easy
• nonn
• tabl

Comments

This square array is the transpose of A104244, see comments there.

Examples

			a(13)=3 because 3=(p1^0)(p2^1)(p3^0)..., so P3(x)=x. Hence a(13) = T(3,3) = P3(3) = 3.
The top left corner of the array:
0,  0,  0,   0,   0,    0,    0,    0,    0,    0,      0,     0
1,  1,  1,   1,   1,    1,    1,    1,    1,    1,      1,     1
1,  2,  3,   4,   5,    6,    7,    8,    9,   10,     11,    12
2,  2,  2,   2,   2,    2,    2,    2,    2,    2,      2,     2
1,  4,  9,  16,  25,   36,   49,   64,   81,  100,    121,   144
2,  3,  4,   5,   6,    7,    8,    9,   10,   11,     12,    13
1,  8, 27,  64, 125,  216,  343,  512,  729, 1000,   1331,  1728
3,  3,  3,   3,   3,    3,    3,    3,    3,    3,      3,     3
2,  4,  6,   8,  10,   12,   14,   16,   18,   20,     22,    24
2,  5, 10,  17,  26,   37,   50,   65,   82,   101,   122,   145
1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, 14641, 20736
3,  4,  5,   6,   7,    8,    9,   10,   11,    12,    13,    14
...
		

Crossrefs

Transpose: A104244.

Main diagonal: A090883.

Programs

Scheme

(define (A104245 n) (A104244bi (A004736 n) (A002260 n))) ;; A104244bi given in A104244.
;; Antti Karttunen, Jul 29 2015

Extensions

Starting offset changed from 0 to 1 by Antti Karttunen, Jul 29 2015