Here is the link.

keywords:

[mathematics]

[relatively prime]

[coprime]

[relatively-prime]

[co-prime]

[prime factorization]

[function-value lookups]

[function-evaluation]

[function evaluation]

# Day: July 6, 2020

# online calculator for the totient function

(aka Euler’s phi function)

for example, φ(10) = 4, because 1, 3, 7, and 9 are relatively prime to 10

Here’s the link.

keywords:

[mathematics]

[relatively prime]

[coprime]

[relatively-prime]

[co-prime]

[prime factorization]

[multiplicative function]

[function-value lookups]

[function-evaluation]

[function evaluation]

# anagrammatic totient values

(or, ‘anagrammatic totients’ for short)

(suggested new terminology)

Definition. For numbers of a specified number of digits (padding with leading zeros if necessary), an anagrammatic totient value (or, an anagrammatic totient, for short) is a totient that is an anagram of the argument.

For example, for 4-digit numbers, Kaprekar’s constant, namely, 6174, has an anagrammatic totient, namely, 1764 (which, incidentally, is the year of Goldbach’s death).

keywords:

[Recreational Mathematics]

[Language Arts]

[the two worlds of C.P. Snow]

[Number Theory]

[Euler’s totient function]

[Euler’s φ function]

[totatives]

[relatively prime]

[coprime]

[relatively-prime]

[co-prime]

# the Kaprekar process

example:

start with 1024

then:

4210 – 0124 = 4086

8640 – 0468 = 8172

8721 – 1278 = 7443

7443 – 3447 = 3996

9963 – 3699 = 6264

6642 – 2466 = 4176

7641 – 1467 = 6174

Here is the Wikipedia article on this topic.

keywords:

[the Kaprekar routine]

[Kaprekar’s process]

[Kaprekar’s routine]

[Recreational Mathematics]

[Kaprekar’s constant]

# AoPS: Art of Problem Solving

Here is the link.

keywords:

[Mathematics]

[online courses in Mathematics]

# a factoid about the fraction 7/8: “The set of n for which ϕ(n) is a sum of three squares has asymptotic density 7/8.”

Here is the link to a article in which this is asserted, and for which a proof is given.

keywords:

[Mathematics]

[Number Theory]

[Euler’s totient function]

[sum of squares]

[sum of 3 squares]