A329288 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.

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, 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, 11, 1, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 12

Offset: 1

Author

Elijah Beregovsky, Feb 16 2020

Keywords

• nonn
• tabl

Comments

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.

Examples

			Table begins:
   1,  1,  1,  1,  1, ...
   2,  2,  2,  2,  2, ...
   3,  3,  3,  3,  3, ...
   4,  5,  5,  5,  5, ...
   5,  5,  5,  5,  5, ...
   6,  7,  7,  7,  7, ...
   7,  7,  7,  7,  7, ...
   8, 11, 11, 11, 11, ...
   9, 11, 11, 11, 11, ...
  10, 11, 11, 11, 11, ...
  11, 11, 11, 11, 11, ...
  12, 15, 17, 17, 17, ...
  13, 13, 13, 13, 13, ...
  14, 15, 17, 17, 17, ...
		

Crossrefs

Cf. A006530 (greatest prime factor), A269304.

Programs

Mathematica

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]