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A076099 Triangle read by rows in which the n-th row contains n numbers not occurring in the previous rows whose product is an n-th power. The first (n-1) numbers of the n-th row are the smallest number not occurring earlier and the n-th term is chosen to satisfy the requirement. 5
1, 2, 8, 3, 4, 18, 5, 6, 7, 9261000, 9, 10, 11, 12, 329422500, 13, 14, 15, 16, 17, 13456677968449745006250, 19, 20, 21, 22, 23, 24, 11022732501667945875061568782593750, 25, 26, 27, 28, 29, 30, 31 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Another rearrangement of the natural numbers in which the product of next n numbers is an n-th power.

The first n-1 elements of the n-th group are the smallest n-1 numbers that haven't already appeared, say u1, u2, ..., u_(n-1) and let u_n be the unknown final element of the n-th group. Let u1*u2*u3*...*u_(n-1) = (p1^e1)(p2^e2)...(pr^er). Then u_n = product(i=1 to r) p_i^(ei + n*floor(ei/n) - n) ...unless this has already appeared in the sequence (probably this never happens). More simply, I conjecture that u_n = product(i=1 to r) p_i^(ei - n). - Sam Alexander, Dec 31 2003

LINKS

Table of n, a(n) for n=0..34.

EXAMPLE

Triangle begins:

1

2 8

3 4 18

5 6 7 9261000

9 10 11 12 329422500

...

CROSSREFS

Cf. A076027, A076028, A076029, A076030, A076031, A076095, A076096, A076097, A076098.

Sequence in context: A076031 A076596 A081967 * A199072 A201748 A011431

Adjacent sequences:  A076096 A076097 A076098 * A076100 A076101 A076102

KEYWORD

nonn,tabl

AUTHOR

Amarnath Murthy, Oct 08 2002

EXTENSIONS

Corrected and extended by Sam Alexander, Dec 31 2003

Edited by Ray Chandler, May 09 2007

STATUS

approved

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Last modified March 26 12:43 EDT 2019. Contains 321497 sequences. (Running on oeis4.)