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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.
2
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).
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 31 2021
STATUS
approved