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⨸ — Factors / Factor spec

Function. Keys: Alt-o u. Hanzi: 因. Ranks: 0 monadic, 0 0 dyadic

⨸N: sorted prime factors, with multiplicity. J’s q: family. Positive whole input. Results take the argument’s domain: ⨸12ᵣ gives [2 2 3]ᵣ.

⨸700                 ⍝ [2 2 5 5 7]ₓ
⨸1                   ⍝ ⍬ₓ
⨸⁻⨸700              ⍝ 700ₓ

Inverse: product. A product of machine integers past 64 bits gives the largest 64-bit integer. K⨸N selects exponents or a factor table.

K Result
Nonnegative whole number Exponents of the first K primes; remaining factors are omitted
∞ Exponents through the largest factor
Negative whole number Last \|K distinct factors and their exponents, in two rows
¯∞ Complete two-row factor/exponent table 
2⨸700                ⍝ [2 0]ₓ
∞⨸700                ⍝ [2 0 2 1]ₓ
¯2⨸700               ⍝ [5 7⋄2 1]ₓ
¯∞⨸700               ⍝ [2 5 7⋄2 2 1]ₓ
0⨸700                ⍝ ⍬ₓ
¯∞⨸1                 ⍝ 2 0⍴0ₓ

Unit cells; results assemble with fill. Large factors follow Prime’s probable-prime policy.

Errors

  • DOMAIN: an N that isn’t positive and whole; a finite K that isn’t whole