|
|
A353510
|
|
Square array A(n,k), n >= 1, k >= 0, with A(n,0) = n, and for k > 0, A(n,k) = A181819(A(n,k-1)), read by descending antidiagonals.
|
|
4
|
|
|
1, 1, 2, 1, 2, 3, 1, 2, 2, 4, 1, 2, 2, 3, 5, 1, 2, 2, 2, 2, 6, 1, 2, 2, 2, 2, 4, 7, 1, 2, 2, 2, 2, 3, 2, 8, 1, 2, 2, 2, 2, 2, 2, 5, 9, 1, 2, 2, 2, 2, 2, 2, 2, 3, 10, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 11, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 12, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 13, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 14
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
The row indexing of this array starts from 1, and the column indexing starts from 0, thus it is read by descending antidiagonals as A(1,0), A(1,1), A(2,0), A(1,2), A(2,1), A(3,0), etc.
A(n, k) gives the k-th prime shadow (the k-fold iterate of A181819) of n.
|
|
LINKS
|
|
|
EXAMPLE
|
The top left {0..6} x {1..16} corner of the array:
1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2,
3, 2, 2, 2, 2, 2, 2,
4, 3, 2, 2, 2, 2, 2,
5, 2, 2, 2, 2, 2, 2,
6, 4, 3, 2, 2, 2, 2,
7, 2, 2, 2, 2, 2, 2,
8, 5, 2, 2, 2, 2, 2,
9, 3, 2, 2, 2, 2, 2,
10, 4, 3, 2, 2, 2, 2,
11, 2, 2, 2, 2, 2, 2,
12, 6, 4, 3, 2, 2, 2,
13, 2, 2, 2, 2, 2, 2,
14, 4, 3, 2, 2, 2, 2,
15, 4, 3, 2, 2, 2, 2,
16, 7, 2, 2, 2, 2, 2,
|
|
MATHEMATICA
|
f[n_] := If[n == 1, 1, Times @@ Prime[FactorInteger[n][[All, -1]]]]; Table[Function[m, Which[m == 1, a[1, k] = 1, k == 0, a[m, 0] = m, True, Set[a[m, k], f[a[m, k - 1]]]]][n - k + 1], {n, 0, 13}, {k, n, 0, -1}] // Flatten (* Michael De Vlieger, Apr 28 2022 *)
|
|
PROG
|
(PARI)
up_to = 105;
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
A353510sq(n, k) = { while(k, n = A181819(n); k--); (n); };
A353510list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, forstep(col=a-1, 0, -1, i++; if(i > up_to, return(v)); v[i] = A353510sq(a-col, col))); (v); };
v353510 = A353510list(up_to);
|
|
CROSSREFS
|
This is a full square array version of irregular triangle A325239, which after 1, lists the terms on each row only up to the first 2.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|