A329288 - OEIS

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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

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OFFSET

1,3

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.

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

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, ...

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]

CROSSREFS

Cf. A006530 (greatest prime factor), A269304.

Sequence in context: A229945 A119585 A195097 * A181845 A183534 A066040

Adjacent sequences: A329285 A329286 A329287 * A329289 A329290 A329291

KEYWORD

nonn,tabl

AUTHOR

Elijah Beregovsky, Feb 16 2020

STATUS

approved