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A076099
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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.
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5
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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; internal format)
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OFFSET
| 0,2
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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 (amnalexander(AT)yahoo.com), Dec 31 2003
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EXAMPLE
| Triangle begins:
1
2 8
3 4 18
5 6 7 9261000
9 10 11 12 329422500
...
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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
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KEYWORD
| nonn,tabl
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 08 2002
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EXTENSIONS
| Corrected and extended by Sam Alexander (amnalexander(AT)yahoo.com), Dec 31 2003
Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), May 09 2007
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