A064555 a(n) = max { k | A064553(k) = n }.

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 319, 317

Offset: 1

Author

Reinhard Zumkeller, Sep 21 2001

Keywords

• nonn
• look

Comments

a(n+1) = A000040(n) for 1 < n < 66, but A000040(65) = 313 <> 319 = 11*29 = a(66).

In the plot, the lowest line corresponds to the cases when a(n)=prime(n-1). - T. D. Noe, Dec 12 2004

a(n) = A080688(n,A001055(n)). - Reinhard Zumkeller, Oct 01 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..8000

Crossrefs

Cf. A064554, A001055, A064553, A000040.

Programs

Haskell

a064555 = last . a080688_row  -- Reinhard Zumkeller, Oct 01 2012

Mathematica

(* b = A064553 *) nmax = 67; b[1] = 1; b[p_?PrimeQ] := b[p] = PrimePi[p] + 1; b[n_] := b[n] = b[p = FactorInteger[n][[1, 1]]]*b[n/p]; bb = Table[{k, b[k]}, {k, 1, 4*Prime[nmax]}]; A064555 = Max[#[[All, 1]]]& /@ Split[ Sort[bb, #1[[2]] < #2[[2]] &], #1[[2]] == #2[[2]]&]; a[n_] := A064555[[n]]; Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Sep 04 2012 *)

Formula

A064553(a(n)) = n and A064553(a(k)) <> k for k > a(n).