%I #28 Mar 19 2020 13:47:58
%S 1,1,2,1,2,3,1,2,3,4,1,2,3,5,5,1,2,3,5,5,6,1,2,3,5,5,7,7,1,2,3,5,5,7,
%T 7,8,1,2,3,5,5,7,7,11,9,1,2,3,5,5,7,7,11,11,10,1,2,3,5,5,7,7,11,11,11,
%U 11,1,2,3,5,5,7,7,11,11,11,11,12
%N Table T(n,k) read by antidiagonals: T(n,k) = f(T(n,k)) starting with T(n,1)=n, where f(x) = x - 1 + x/gpf(x), that is, f(x) = A269304(x)-2.
%C If p=T(n,k0) is prime, then T(n,k) = p - 1 + p/p = p for k > k0. Thus, primes are fixed points of this map. The number of different terms in the n-th row is given by A330437.
%e Table begins:
%e 1, 1, 1, 1, 1, ...
%e 2, 2, 2, 2, 2, ...
%e 3, 3, 3, 3, 3, ...
%e 4, 5, 5, 5, 5, ...
%e 5, 5, 5, 5, 5, ...
%e 6, 7, 7, 7, 7, ...
%e 7, 7, 7, 7, 7, ...
%e 8, 11, 11, 11, 11, ...
%e 9, 11, 11, 11, 11, ...
%e 10, 11, 11, 11, 11, ...
%e 11, 11, 11, 11, 11, ...
%e 12, 15, 17, 17, 17, ...
%e 13, 13, 13, 13, 13, ...
%e 14, 15, 17, 17, 17, ...
%t Clear[f,it,order,seq]; f[n_]:=f[n]=n-1+n/FactorInteger[n][[-1]][[1]]; it[k_,n_]:=it[k,n]=f[it[k,n-1]]; it[k_,1]=k; SetAttributes[f,Listable]; SetAttributes[it,Listable]; it[#,Range[10]]&/@Range[800]
%Y Cf. A006530 (greatest prime factor), A269304.
%K nonn,tabl
%O 1,3
%A _Elijah Beregovsky_, Feb 16 2020