A104245 - OEIS

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

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OFFSET

1,9

COMMENTS

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

LINKS

Table of n, a(n) for n=1..95.

EXAMPLE

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

...

PROG

(Scheme)

(define (A104245 n) (A104244bi (A004736 n) (A002260 n))) ;; A104244bi given in A104244.

;; Antti Karttunen, Jul 29 2015

CROSSREFS

Transpose: A104244.

Main diagonal: A090883.

Sequence in context: A170982 A296339 A362686 * A185287 A276554 A297323

Adjacent sequences: A104242 A104243 A104244 * A104246 A104247 A104248

KEYWORD

easy,nonn,tabl

AUTHOR

Olaf Voß, Feb 26 2005

EXTENSIONS

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

STATUS

approved