login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
EXAMPLE
Triangle begins:
1
2 8
3 4 18
5 6 7 9261000
9 10 11 12 329422500
...
CROSSREFS
Sequence in context: A076031 A076596 A081967 * A199072 A201748 A011431
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)