factor(x+1)

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

I think I am looking for a decent data-structure
to store a factor(x+1) tree.
But if you see a different angle on it, don't hesitate.

I'm considering Vec-of-Vec, to mean something like (vecprod(v)-1).


Example:
- - - -
N=9781262575275081247; \
apply(Vec,Vec(factor(N+1)~))

[ [2, 5]
, [19, 1]
, [1987, 1]
, [1038209, 1]
, [7798457, 1]
]


Manual transformations:
(so beware of tpyos)

[ [2, 5]                \\ 2^5
, [[ [2,2], 5 ]]        \\ (2^2*5 -1)
, [[ [2,2], 7, 71 ]]    \\ (2^2*7*71 -1)
, [[ 2, 3, 5, 34607 ]]  \\ (2*3*5*34607 -1)
, [[ 2, 3, 1299743 ]]   \\ (2*3*1299743 -1)
]

[ [2, 5]                \\ 2^5
, [[ [2,2], [[2,3]] ]]  \\ 2^2*(2*3-1)
, [[ [2,2], [[ [2,3] ]], [[ [2,3],[3,2] ]] ]]
                        \\ 2^2*(2^3-1)*(2^3*3^2-1)
, [[ 2,3, [[2,3]], [[ [2,4], 3, 7, 103 ]] ]]
                        \\ 2*3*(2*3-1)*(2^4*3*7*103-1)
, [[ 2,3, [[ [2,5], [3^2], 4513 ]]
                        \\ 2*3*(2^5*3^2*4513-1)
]

103
-> 2^3*13
-> 2^3*(2*7-1)
-> 2^3*(2*(2^3-1)-1)

4513
-> 2*37*61
-> 2*(2*19-1)*(2*31-1)
-> 2*(2^2*5-1)*(2*(2^5-1)-1)
-> 2*(2^2*(2*3-1)-1)*(2*(2^5-1)-1)
- - - -


-- Ruud