[seqfan] Re: Happy 3³+4³+5³+6³+7³+8³+9³

[Sven Simon]

That should read correctly 2025 = 1³+2³+3³+4³+5³+6³+7³+8³+9³ = (1+2+3+4+5+6+7+8+9)**2
The text format changed, the exponent was written like normal text after sending, on my screen it was still ok.
Sven

-----Ursprüngliche Nachricht-----
Von: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] Im Auftrag von Sven Simon
Gesendet: Sonntag, 31. Januar 2016 11:15
An: 'Sequence Fanatics Discussion list'
Betreff: [seqfan] Re: Happy 3³+4³+5³+6³+7³+8³+9³

So 2025 we have

 

2025 = 1³+2³+3³+4³+5³+6³+7³+8³+9³ = (1+2+3+4+5+6+7+8+9)2

 

 

 

-----Ursprüngliche Nachricht-----
Von: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] Im Auftrag von Veikko Pohjola
Gesendet: Samstag, 30. Januar 2016 19:20
An: Sequence Fanatics Discussion list
Betreff: [seqfan] Re: Happy 3³+4³+5³+6³+7³+8³+9³

 

Dear Giovanni and others,

 

The French have a custom to send New Year's greetings at the end of January. So I got the idea to play a little with the charming geometrical problem, number 7 below. The side lengths of the triangles, where all the sides are integral and satisfy the condition of green squares x+y=z, form each a nice sequence as the triangle grows. The smallest side goes like this: 13,17,25,37,41,53,61, …

 

Happy New Year,

Veikko Pohjola

 

Giovanni Resta kirjoitti 4.1.2016 kello 10.59:

 

> Other notable properties of 2016:

> 

> (1) The middle value y of the smallest amicable triple, i.e., 3 numbers x < y < z such that sigma(x)=sigma(y)=sigma(z) = x+y+z \sigma(n) is the sum of the divisors of n.

> 

> (2) The only number n such that n^3 + n^2 is strictly pandigital, i.e., it contains all the digits 0 to 9 exactly once.

> 

> (3) The smallest number equal to the sum of its 31 smallest divisors.

> 

> (4) The smallest number whose square root begins with 10 composite digits (so 4, 6, 8 or 9).

> 

> (5) If p(n) denotes the n-th prime number, the product of digits of p(p(666)) is 2016.

> 

> (6) T(rev(iT(2016))) = 666, where T(n) is the n-th triangular number, rev(n) is the reverse of n, and iT(T(n))=n.

> 

> (7) The value of y in this geometrical problem  <http://www.numbersaplenty.com/prob2016.png> http://www.numbersaplenty.com/prob2016.png

> 

> Giovanni Resta

> 

> 

> _______________________________________________

> 

> Seqfan Mailing list -  <http://list.seqfan.eu/> http://list.seqfan.eu/

 

 

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