| Prime Factors | q: 0 0 0 | Prime Exponents |
q: y is the list of prime factors of a positive integer
argument y . For example:y=: 105600 q: y 2 2 2 2 2 2 2 3 5 5 11 */q: y 105600 $ q: 1 0 */q: 1 1 q: b. _1 */ |
If x is positive and finite, x q: y
is the list of exponents in the prime decomposition of positive
integer y, based upon the first x primes;
if x is _ , a sufficient number
of primes is used. If x is negative and finite, x q: y is a 2-row table of the last |x primes and exponents in the prime factorization of y ; if x is __ , a sufficient number of primes is used. For example: 2 q: 700 2 0 10 q: 700 2 0 2 1 0 0 0 0 0 0 _ q: 700 2 0 2 1 |
~.@q: 700 Distinct prime factors 2 5 7 +/"1@=@q: 700 Exponents in prime factorization 2 2 1 __ q: 700 2 5 7 2 2 1 _q: !20x 2 3 5 7 11 13 17 19 18 8 4 2 1 1 1 1 y=: 100 e=: _&q: Completed list of exponents (e ; +:&.e ; -:&.e ; %&3&.e)y Exponents, square, sqrt, cube root +-----+-----+--+-------+ |2 0 2|10000|10|4.64159| +-----+-----+--+-------+ V=: /@,: For vectors of disparate lengths 12 (+V&.e; -V&.e; >.V&.e; <.V&.e) y Product, quotient, LCM, GCD +----+----+---+-+ |1200|0.12|300|4| +----+----+---+-+ totient=: * -.@%@~.&.q: Euler's totient function totient 700 240 +/ 1 = 700 +. i.700 240