The Hidden Ciruit
The Sacred Niven Harmonic Series: 36,72,108,144,216,252,288,324,360,396,432,468,504,540,576
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~36~
Note: D0
36 is the square of 6 and the smallest triangular number other than 1. It is the only triangular number whose square root is also a triangular number.
17+19=36
3x12=36
9x4=36
6x6=36
It is the also the smallest number with exactly 8 solutions to the equation φ(x) = n. Being the smallest number with exactly 9 divisors, 36 is a highly composite number. Adding up some subsets of its divisors (6, 12 and 18) gives us 36, showing its mathematical symmetry, and its relationship to the golden ratio.
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~72~
Note: D1
The Number of Tarot Keys
8×9=72 the second harmonic
The second harmonic 72, is the sum of four consecutive primes (13 + 17 + 19 + 23), as well as the sum of six consecutive primes (5 + 7 + 11 + 13 + 17 + 19). The product of 8 and 9, 72 is a pronic (or hexagonal) number relating this number to the mobious function [μ(x) = μ(n) μ(n + 1)]. As a multiple of a perfect number, 72 is itself a semi-perfect number. Its factors show the golden proportion 2cubed and 3squared.
72 is the smallest number whose fifth power is the sum of 5 smaller fifth powers; 195 + 435 + 465 + 475 + 675 = 725
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~108~
Note: A2
The number of prayer beads in a mala.
108 is a number that is divisible by the value of its φ function, which is 36. 108 is also divisible by the total number of its divisors (12), hence it is a refactorable number.
In Euclidean space, the interior angles of a regular pentagon measure 108 degrees each.
There are 108 free polynomials of order 7.
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~144~
Note: D2
“I will sing you a new song, O God,
on the ten-stringed lute will I sing your praises.” ~Psalms 144, verse 9
It is the twelfth Fibonacci number, and the largest one to also be a square,[1] as the square of 12 (which is also its index in the Fibonacci sequence), following 121 and preceding 169.
144 is the smallest number with exactly 15 divisors.
144 is a number that is divisible by the value of its φ function, which returns 48 in this case. Also, there are 21 solutions to the equation φ(x) = 144, more than any integer below 144, making it a highly totient number.
1445 = 275 + 845 + 1105 + 1335, the smallest number whose fifth power is a sum of four (smaller) fifth powers.
The maximum determinant in a 9 by 9 matrix of zeroes and ones is 144.
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~180~
Note: F#2
The sum of six consecutive primes (19 + 23 + 29 + 31 + 37 + 41) The sum of eight consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37) The sum of Euler’s totient function φ(x) over the first twenty-four integers is 180 Using degrees (°) to measure angles, 180° is called straight angle 180° is equivalent to π rads. In normal space, the interior angles of a triangle add up to 180°
180 is a Harshad number in base 10
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~216~
Note: A3
Since 216 = 33 + 43 + 53 = 63, it is the smallest cube that’s also the sum of three cubes (Plato was among the first to notice this, and mentioned it in Book VIII of Republic). It is also the sum of a twin prime (107 + 109). But since there is no way to express it as the sum of the proper divisors of any other integer, it is an untouchable number.
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~252~
12×21
“Square Number”
In mathematics, a square number, sometimes also called a perfect square, is an integer that can be written as the square of some other integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3. Square numbers are non-negative. Another way of saying that a (non-negative) number is a square number, is that its square root is again an integer. For example, √9 = 3, so 9 is a square number.
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288
Note:D3
32×9
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~324~
Note: E3
324 is the smallest untouchable square.
Definition: The untouchable numbers are those that are not the sum of the proper divisors of any number.
First ten: 2, 5, 52, 88, 96, 120, 124, 146, 162, 188.
There are 1212 untouchable numbers below 10,000.
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~432~
Note: A4
Tags: 36Hz, 396, 44Hz, circuit, energy, King, Queen, scales, solfeggio
