A double 34 for my post number. So is there anything significant about the number 34? Well let's check Wikipedia...
34 is the ninth distinct semiprime and has four divisors including one and itself. Its neighbors, 33 and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has. It is also in the first cluster of three distinct semiprimes, being within 33, 34, 35; the next such cluster of semiprimes is 85, 86, 87.
It is the ninth Fibonacci number[1] and a companion Pell number.[2] Since it is an odd-indexed Fibonacci number, 34 is a Markov number, appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.
This number is the magic constant of a 4 by 4 normal magic square:[3]
It has the aliquot sum, 20, in the following descending sequence 34,20,22,14,10,8,7,1. and it is the 6th composite member of the 7-aliquot tree.
There is no solution to the equation φ(x) = 34, making 34 a nontotient.[5] Nor is there a solution to the equation x − φ(x) = 34, making 34 a noncototient.[6]
I left all the links from Wikipedia active. Just in case you want to find out more about aliquot sums, totient and nontotient numbers, and semiprimes! Who could resist?! I know I'm heading for the heptagonal numbers now.
Auh oh. I just realized today is Friday the 13th too. When Friday the 13th falls on a Tuesday it means double trouble. Maybe since 13 is a Fibonacci number and 34 is a heptagonal number they will cancel each other out. One can only hope.
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3 comments:
That's a lot of info about the number 34!
Right.....
A great discourse on 34.
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