TINT Package Info TINT, or TI Number Theory, is a package of lists and programs designed for number theoretic computation and analysis on the TI-84+ series of calculators. These programs are designed to be used as subprograms for larger projects, and are optimized for numbers less than 10^12. Note: This package requires OS 2.53MP or higher to use. A version for older calculator models will be available soon. To install, simply download and open the group. All TINT programs are denoted by θNT followed by 2 or 3 characters. The following variables and lists are defined for an input N after executing the program θNTN. Most programs also require the factorization of N to be defined via θNTN (exceptions are noted below). Vars Properties -W: Count of distinct prime divisors -O: Count of prime divisors -C: Compositeness -T: # of Divisors -S: Sum of Divisors -A: Aliquot -B: Abundance -H: Totient -L: Liouville function -U: Mobius function -R: Radical -D: Arithmetic derivative -G: Log arithmetic derivative Inputs -N: Number -P: Arbitrary prime -M: Arbitrary whole number (usually a modulus) -Q: Arbitrary whole number -K: Input number (usually small) Program Vars -X: Bound -Y: Loop var -Z: Counter Empty Vars -E: Empty var -F: Empty var -I: Empty var -J: Empty var -V: Empty var -θ: Empty var Lists -P: Prime factors of N -A: Prime multiplicities of N -B: A+1 -D: Divisors of N -E: Divisor multiplicities of N -U: Unitary divisors of N Premade Lists -P100: All primes < 100 -P1000: All primes < 1000 Programs (return is Ans unless otherwise stated) -NTCM: Carmichael's function of N -NTCQ: Ramanujan's sum of N base Q -NTCR: Core of N mod M -NTDK: Sum of Kth powers of divisors of N -NTGCD: GCD of L1 -NTIS: If N satisfies property; input the property as a two-letter string from the list below in Ans --"CM": Carmichael --"LC": Lucas-Carmichael --"KP": K-Perfect --"GI": Giuga --"SF": Squarefree --"KS": K-Smooth --"KR": K-Rough --"PW": Perfect power --"AB": Abundant --"PF": Powerful --"UN": Unusual --"RF": Refactorable --"SP": Semiprime --"NH": Nonhypotenuse --"AP": Almost perfect --"KH": K-Hyperperfect --"HP": Hemiperfect --"BL": Blum --"RG": Regular --"HD": Harmonic divisor --"AR": Arithmetic --"PP": Primary pseudoperfect -NTJK: Jordan's totient of N base K -NTLCM: LCM of L1 -NTLI: Intersection of L1 and L2 --> L3 -NTLJ: Kronecker symbol (generalized Legendre/Jacobi symbol) of N base Q -NTMO: Multiplicative order of Q mod M -NTMU: Mobius function of N w/o factorization -NTMX: Q^K mod M (modular exponentiation algorithm) -NTN: TINT data initialization for N -NTPF: Prime factorization of N -NTPG: List of primes up to X --> L1 -NTPN: Generate next prime given a list of previous primes in L1 -NTPT: Primality test of N w/o factorization -NTVP: Multiplicity of P in N Have any questions? Found a bug? Contact kg583 on TI-Basic Developer. Copyright © Kevin Gomez 2018. All rights reserved.