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A146756 Smallest numbers expressible as the sum of n distinct positive n-th powers in exactly n ways. 4
1, 65, 5104, 300834, 9006349824 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Contribution from 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)

If duplicate n-th powers were allowed, a(2) would be 50. - Jonathan Sondow, Oct 23 2013

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

for n=2, 65= 1^2 + 8^2 = 4^2 + 7^2

CROSSREFS

Cf. A230477 (same except that the n-th powers need not be distinct and the number of ways is at least n, not necessarily exactly n). - Jonathan Sondow, Oct 23 2013

Sequence in context: A027535 A110900 A084272 * A202386 A115432 A116104

Adjacent sequences:  A146753 A146754 A146755 * A146757 A146758 A146759

KEYWORD

hard,more,nonn

AUTHOR

Ian Rayson (Ian.Rayson(AT)studentmail.newcastle.edu.au), Nov 02 2008

EXTENSIONS

a(5) from Donovan Johnson, Nov 08 2008

Definition clarified by Jonathan Sondow, Oct 23 2013

STATUS

approved

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Last modified September 20 17:56 EDT 2014. Contains 247018 sequences.