cp's OEIS Frontend

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.

%I A353510 #12 Apr 28 2022 09:43:14
%S A353510 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,
%T A353510 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,
%U A353510 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
%N 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.
%C A353510 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.
%C A353510 A(n, k) gives the k-th prime shadow (the k-fold iterate of A181819) of n.
%H A353510 Michael De Vlieger, <a href="/A353510/b353510.txt">Table of n, a(n) for n = 1..11476</a> (rows n = 1..150, flattened)
%e A353510 The top left {0..6} x {1..16} corner of the array:
%e A353510    1, 1, 1, 1, 1, 1, 1,
%e A353510    2, 2, 2, 2, 2, 2, 2,
%e A353510    3, 2, 2, 2, 2, 2, 2,
%e A353510    4, 3, 2, 2, 2, 2, 2,
%e A353510    5, 2, 2, 2, 2, 2, 2,
%e A353510    6, 4, 3, 2, 2, 2, 2,
%e A353510    7, 2, 2, 2, 2, 2, 2,
%e A353510    8, 5, 2, 2, 2, 2, 2,
%e A353510    9, 3, 2, 2, 2, 2, 2,
%e A353510   10, 4, 3, 2, 2, 2, 2,
%e A353510   11, 2, 2, 2, 2, 2, 2,
%e A353510   12, 6, 4, 3, 2, 2, 2,
%e A353510   13, 2, 2, 2, 2, 2, 2,
%e A353510   14, 4, 3, 2, 2, 2, 2,
%e A353510   15, 4, 3, 2, 2, 2, 2,
%e A353510   16, 7, 2, 2, 2, 2, 2,
%t A353510 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 *)
%o A353510 (PARI)
%o A353510 up_to = 105;
%o A353510 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A353510 A353510sq(n, k) = { while(k, n = A181819(n); k--); (n); };
%o A353510 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); };
%o A353510 v353510 = A353510list(up_to);
%o A353510 A353510(n) = v353510[n];
%Y A353510 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.
%Y A353510 Columns 0..2: A000027, A181819, A328830.
%Y A353510 Rows 1..2: A000012, A007395.
%K A353510 nonn,tabl
%O A353510 1,3
%A A353510 _Antti Karttunen_ and _Gus Wiseman_, Apr 27 2022