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Revision History for A146756 (Underlined text is an addition; strikethrough text is a ~~deletion~~.)
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A146756

a(n) is the smallest number expressible as the sum of n distinct positive n-th powers in exactly n ways.
(history; published version)

#29 by N. J. A. Sloane at Wed Dec 22 02:58:30 EST 2021

STATUS

editing

approved

#28 by N. J. A. Sloane at Wed Dec 22 02:58:25 EST 2021

COMMENTS

It is not known if any terms exist in this sequence beyond n = 46.

STATUS

proposed

editing

#27 by Jinyuan Wang at Wed Dec 22 02:54:35 EST 2021

STATUS

editing

proposed

Discussion
Wed Dec 22	02:57	N. J. A. Sloane: It is EXTREMELY confusing to see the first comment. Let's change it to n=6

#26 by Jinyuan Wang at Wed Dec 22 02:53:35 EST 2021

COMMENTS

ContributionPer email communication from _ Ian Rayson, the n-th powers for each sum must be distinct. If duplicate n-th powers were allowed, a(4) would be 236674 while the other terms would remain unchanged. - _Donovan Johnson_, Nov 08 2008: (Start)

a(5) = 9006349824 = 8^5 + 34^5 + 62^5 + 68^5 + 92^5 = 8^5 + 41^5 + 47^5 + 79^5 + 89^5 = 12^5 + 18^5 + 72^5 + 78^5 + 84^5 = 21^5 + 34^5 + 43^5 + 74^5 + 92^5 = 24^5 + 42^5 + 48^5 + 54^5 + 96^5.

Per email communication from Ian Rayson, the n-th powers for each sum must be distinct. If duplicate n-th powers were allowed, a(4) would be 236674 while the other terms would remain unchanged. (End)

From Michael S. Branicky, Dec 21 2021: (Start)

a(6) = 82188309244 = 1^6 + 9^6 + 29^6 + 44^6 + 55^6 + 60^6,

= 2^6 + 12^6 + 25^6 + 51^6 + 53^6 + 59^6,

= 5^6 + 23^6 + 27^6 + 44^6 + 51^6 + 62^6,

= 10^6 + 16^6 + 41^6 + 45^6 + 51^6 + 61^6,

= 12^6 + 23^6 + 33^6 + 34^6 + 55^6 + 61^6,

= 15^6 + 23^6 + 31^6 + 36^6 + 53^6 + 62^6. (End)

EXAMPLE

For n=a(2, ) = 65 = 1^2 + 8^2 = 4^2 + 7^2.

a(5) = 9006349824 = 8^5 + 34^5 + 62^5 + 68^5 + 92^5 = 8^5 + 41^5 + 47^5 + 79^5 + 89^5 = 12^5 + 18^5 + 72^5 + 78^5 + 84^5 = 21^5 + 34^5 + 43^5 + 74^5 + 92^5 = 24^5 + 42^5 + 48^5 + 54^5 + 96^5. - Donovan Johnson, Nov 08 2008

From Michael S. Branicky, Dec 21 2021: (Start)

a(6) = 82188309244 = 1^6 + 9^6 + 29^6 + 44^6 + 55^6 + 60^6,

= 2^6 + 12^6 + 25^6 + 51^6 + 53^6 + 59^6,

= 5^6 + 23^6 + 27^6 + 44^6 + 51^6 + 62^6,

= 10^6 + 16^6 + 41^6 + 45^6 + 51^6 + 61^6,

= 12^6 + 23^6 + 33^6 + 34^6 + 55^6 + 61^6,

= 15^6 + 23^6 + 31^6 + 36^6 + 53^6 + 62^6. (End)

STATUS

proposed

editing

#25 by Jon E. Schoenfield at Wed Dec 22 00:23:45 EST 2021

STATUS

editing

proposed

Discussion
Wed Dec 22	00:25	Michael S. Branicky: Yes!
	01:54	Michel Marcus: move a(6) = 82188309244 = 1^6 + 9^6 + 29^6 + 44^6 + 55^6 + 60^6 etc to example ?

#24 by Jon E. Schoenfield at Wed Dec 22 00:22:46 EST 2021

NAME

Smallesta(n) is the smallest numbersnumber expressible as the sum of n distinct positive n-th powers in exactly n ways.

STATUS

proposed

editing

Discussion
Wed Dec 22	00:23	Jon E. Schoenfield: The existing Name looked as though this was a "list" (numbers with a given property). This edit reflects the intent, right?

#23 by Michael S. Branicky at Tue Dec 21 22:32:20 EST 2021

STATUS

editing

proposed

Discussion
Tue Dec 21	23:16	Jinyuan Wang: I see, then keep "n=4" is okk

#22 by Michael S. Branicky at Tue Dec 21 22:32:12 EST 2021

COMMENTS

a(6) = 82188309244 = 1^6 + 9^6 + 29^6 + 44^6 + 55^6 + 60^6,

= = 2^6 + 12^6 + 25^6 + 51^6 + 53^6 + 59^6,

= = 5^6 + 23^6 + 27^6 + 44^6 + 51^6 + 62^6,

= = 10^6 + 16^6 + 41^6 + 45^6 + 51^6 + 61^6,

= = 12^6 + 23^6 + 33^6 + 34^6 + 55^6 + 61^6,

= = 15^6 + 23^6 + 31^6 + 36^6 + 53^6 + 62^6. (End)

STATUS

proposed

editing

#21 by Michael S. Branicky at Tue Dec 21 22:30:35 EST 2021

STATUS

editing

proposed

#20 by Michael S. Branicky at Tue Dec 21 22:30:31 EST 2021

COMMENTS

It is not known if any terms exist in this sequence beyond n=6 = 4.

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Last modified August 30 15:13 EDT 2024. Contains 375545 sequences. (Running on oeis4.)