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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
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
Michael De Vlieger, Table of n, a(n) for n = 1..11476 (rows n = 1..150, flattened)
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);
A353510(n) = v353510[n];
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.
Columns 0..2: A000027, A181819, A328830.
Rows 1..2: A000012, A007395.
Sequence in context: A333486 A128628 A238966 * A334230 A275723 A198338
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen and Gus Wiseman, Apr 27 2022
STATUS
approved