A347388 The first 3-smooth number eventually reached when iterating Dedekind psi function from n, with a(n) = n if n is already a 3-smooth number.

1, 2, 3, 4, 6, 6, 8, 8, 9, 18, 12, 12, 24, 24, 24, 16, 18, 18, 36, 36, 32, 36, 24, 24, 72, 96, 27, 48, 72, 72, 32, 32, 48, 54, 48, 36, 144, 144, 96, 72, 96, 96, 72, 72, 72, 72, 48, 48, 96, 216, 72, 192, 54, 54, 72, 96, 144, 216, 144, 144, 96, 96, 96, 64, 192, 144, 108, 108, 96, 144, 72, 72, 576, 576, 288, 288, 96, 384

Offset

1,2

Comments

See comments and references in A019269, which gives the number of iterations needed to reach a(n).

Links

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

Formula

If A006530(n) <= 3, then a(n) = n, otherwise a(n) = a(A001615(n)).

Mathematica

psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); a[n_] := NestWhile[psi, n, FactorInteger[#][[-1, 1]] > 3 &]; Array[a, 100] (* Amiram Eldar, Aug 31 2021 *)

Prog

(PARI)
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A347388(n) = if(A006530(n)<=3, n, A347388(A001615(n)));

Crossrefs

Cf. A001615, A003586, A006530, A019269, A065333.

Cf. also A347387.

Sequence in context: A350786 A134361 A142727 * A112275 A335876 A306974

Adjacent sequences: A347385 A347386 A347387 * A347389 A347390 A347391

Keyword

nonn

Author

Antti Karttunen, Aug 31 2021

Status

approved