%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