n! = Factorial - n x (n-1) x (n-2) x …. x 3 x 2 x 1
n!! = Double Factorial - n x (n-2) x (n-4) x … x either (6 x 4 x 2) or (5 x 3 x 1)
Γn = Gamma function - (n-1)!
⌈n⌉ = Ceiling function - the smallest integer equal to or greater than n
⌊n⌋ = Floor function - the largest integer equal to or smaller than n
n# = Primorial - n! but only using the prime numbers
n$ = Superfactorial - n! x (n-1)! x (n-2)! x … x 3! x 2! x 1!
τ(n) = Ramanujan’s Tau function – can't explain this one but it exists and the list up to τ(28) is here:
http://oeis.org/A000594/list
σ(n) = Divisor function – sum of all factors of n
Π(n) = Prime counting function – how many prime numbers exist up to and including n
μ(n) = Mobius function – if the number is a square it's 0, if the number is not a square and Π(n) is odd it's -1, and if it's not a square and Π(n) is even it's 1. List to μ(77) here:
http://oeis.org/A008683/list (not incredibly useful except it gives us a single 5 way to get to 1 - μ(5!!) - so could come in handy now and then)
Σ(n) = Sum function – n + (n-1) + (n-2) + …… + 3 + 2 + 1
φ(n) = Euler’s totient function – number of numbers less than n which share no factors with n – list up to φ(69) here:
http://oeis.org/A000010/list
σ(n) = the number of distinct primes that are factors of n. List up to σ(111) here:
http://oeis.org/A001221/list (again not greatly useful except as a single 5 way to get to 2 - σ(5!!))
