# pau'au VUhU3 experimental cmavo

ternary mekso operator: p-adic valuation; outputs (positive) infinity if x1 = 0 and, else, outputs sup(Set(k: k is a nonnegative integer, and ((1 - x3)x divides x1)), where pn is the nth prime (such that p1 = 2).

The terbri order here was defined in analogy to "de'o". Normally, x1 should be a rational number, and x2 should be a positive integer; some generalizations may be possible, though. x3 is either 0 xor 1, and indicates/toggles between modes: x3 = 0 yields the x2-adic valuation (even for nonprime x2); x3 = 1 yields the px-adic valuation. x2 = 1, x3 = 0 yields positive infinity for any x1 which is within the domain. If x1 = n/m and is a rational noninteger number such that gcd(n,m) = 1, then pau'au(x1, x= pau'au(n, x2, x pau'au(m, x2, x. See also: "fei'i", "pi'ei'oi". This word is often equivalent to or closely related to "1 divided by X2 in algebraic structure X3">pei'e'a" (which is, in some ways, more general but also is less flexible with respect to its input).

## In notes:

fei'i (exp!)
mekso variable-arity (at most ternary) operator: number of prime divisors of number X1, counting with or without multiplicity according to the value X2 (1 xor 0 respectively; see note for equality to -1 and for default value), in structure X3.
pi'ei'oi (exp!)
mathematical ternary operator: prime-generating function.