triperfect.
 

[QUOTE=Kees]Forgot to post a "special number", so here goes

672[/QUOTE]

672 number is the 2nd triperfect number after 120
672 =2^5 * 3 * 7
Sum of divisors is 3 *672 = 2016
There are I believe only 6 of this kind.
Sorry Richard C. you have the book too.
Mally :coffee:

A very interesting number 729.

Mally :coffee:

[QUOTE=mfgoode]672 number is the 2nd triperfect number after 120
672 =2^5 * 3 * 7
Sum of divisors is 3 *672 = 2016
There are I believe only 6 of this kind.
Sorry Richard C. you have the book too.
Mally :coffee:

A very interesting number 729.

Mally :coffee:[/QUOTE]
729 is 3^6. Also, 7+2=9, and 7 and 2 are primes.

Next number: 129

edit: there are two things special about 129.

5^3+2^2=129 --> sum of 2 powers
and 2^7+1 =129
and 2^7+1/3 is prime 2^7-1 is prime and 7=4^1+3 is prime. This supports the new mersenne conjecture.

New number 251.

[QUOTE=Citrix]5^3+2^2=129 --> sum of 2 powers
and 2^7+1 =129
and 2^7+1/3 is prime 2^7-1 is prime and 7=4^1+3 is prime. This supports the new mersenne conjecture.

New number 251.[/QUOTE]
Actually, the special parts that I had in mind were 2^7+1=129 (which you got) and that the sum of the first 10 primes = 129.

The sum of 2 powers was also interesting, though.

251 will for me stay the flatnumber of an ex-girlfriend, but otherwise, it is the sum of one, three and seven consecutive primes

new number: 132 (no insult intended):cat:

Number 129
 

[QUOTE=MooooMoo]729 is 3^6. Also, 7+2=9, and 7 and 2 are primes.

Next number: 129

edit: there are two things special about 129.[/QUOTE]

:smile: The number 129 is the sum of 3 powers in 4 different ways.
I give the first two

129 = 2^2 + 5^2 + 10^2

129 = 2 ^2 + 2^2 + 11^2

I leave the remaining two ways to you

Mally :coffee:

Number 251
 

[QUOTE=Citrix]5^3+2^2=129 --> sum of 2 powers
and 2^7+1 =129
and 2^7+1/3 is prime 2^7-1 is prime and 7=4^1+3 is prime. This supports the new mersenne conjecture.

New number 251.[/QUOTE]

:smile: Number 251 = the sum of 3 cubes in 2 ways.

I give the first way 251 = 5^3 + 5^3 + 1^3

Mally :coffee:

No. 132.
 

[QUOTE=Kees]251 will for me stay the flatnumber of an ex-girlfriend, but otherwise, it is the sum of one, three and seven consecutive primes

new number: 132 (no insult intended):cat:[/QUOTE]

132 = the sum of all 2 digit no.s made from its digits

132 = 13 +32 +21 +31 +23 +12

It is the smallest such number.

Mally :coffee:

277

For 251 I was looking for 2*251^251+1 is prime. I found it a couple of years ago.:coffee:

[QUOTE=mfgoode]:smile: The number 129 is the sum of 3 powers in 4 different ways.
I give the first two

129 = 2^2 + 5^2 + 10^2

129 = 2 ^2 + 2^2 + 11^2

I leave the remaining two ways to you

Mally :coffee:[/QUOTE]
129 = 4^2 + 7^2 + 8^2

129 = 4^2 +2^5 + 9^2

[QUOTE=MooooMoo]129 = 4^2 + 7^2 + 8^2

129 = 4^2 +2^5 + 9^2[/QUOTE]

:razz
Actually I meant the sum of 3 squares in 4 different ways.
So we get the 4th as
129 = 8^2 + 8^2 + 1^2

Mally :coffee: