# online calculator for the Carmichael function

Here is the link. keywords: [mathematics] [relatively prime] [coprime] [relatively-prime] [co-prime] [prime factorization] [function-value lookups] [function-evaluation] [function evaluation]

# 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 … Continue reading anagrammatic totient values

# 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 … Continue reading the Kaprekar process

# 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]