⨸ — Factor

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

⨸N: sorted prime factors, with multiplicity. J’s q: family. Positive integral input; exact integer results.

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

Inverse: product. K⨸N selects exponents or a factor table.

K	Result
Nonnegative integer	Exponents of the first K primes; remaining factors are omitted
∞	Exponents through the largest factor
Negative integer	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: nonpositive/non-integral N; non-integral finite K