

A076099


Triangle read by rows in which the nth row contains n numbers not occurring in the previous rows whose product is an nth power. The first (n1) numbers of the nth row are the smallest number not occurring earlier and the nth 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
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OFFSET

0,2


COMMENTS

Another rearrangement of the natural numbers in which the product of next n numbers is an nth power.
The first n1 elements of the nth group are the smallest n1 numbers that haven't already appeared, say u1, u2, ..., u_(n1) and let u_n be the unknown final element of the nth group. Let u1*u2*u3*...*u_(n1) = (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



