A340324 Numbers k such that starting with k and repeatedly applying the map x -> A340323(x) reaches the loop {3, 4}.

2, 3, 4, 7, 8, 9, 16, 21, 27, 31, 32, 63, 64, 81, 93, 127, 128, 189, 217, 243, 256, 279, 381, 512, 567, 651, 729, 837, 889, 1024, 1143, 1701, 1953, 2048, 2187, 2511, 2667, 3429, 3937, 4096, 5103, 5859, 6561, 7533, 8001, 8191, 8192, 10287, 11811, 15309, 16384

Offset

1,1

Comments

From Sebastian Karlsson, Jan 15 2021: (Start)

The sequence can be defined exclusively as:

- Powers of two greater than one.

- Powers of three greater than one.

- Products of distinct Mersenne primes (A046528, except initial 1) or powers of three multiplied with products of distinct Mersenne primes. (End)

Links

Table of n, a(n) for n=1..51.

Mathematica

fa[n_]:=fa[n]=FactorInteger[n]; phi[1]=1; phi[p_, s_]:= (p + 1)*( p - 1)^(s - 1)
phi[n_]:=Product[phi[fa[n][[i, 1]], fa[n][[i, 2]]], {i, Length[fa[n]]}];
S[n_] := NestWhile [phi, n, ! ( # == 12 || # == 3 || # == 4) &];
Select[1 + Range[100], 2<S[#]<5 &]

Prog

(PARI) f(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, (f[i, 1]+1)*((f[i, 1]-1)^(f[i, 2]-1)))); \\ A340323
isok(m) = if (m==1, return(0)); while(! ((m==3) || (m==4) || (m==12)), m = f(m)); ((m==3) || (m==4)); \\ Michel Marcus, Jan 21 2021

Crossrefs

Cf. A340323, A340325.

Cf. A000079, A000244, A000668, A046528.

Sequence in context: A329295 A058075 A243495 * A029783 A112736 A059930

Adjacent sequences: A340321 A340322 A340323 * A340325 A340326 A340327

Keyword

nonn

Author

José María Grau Ribas, Jan 05 2021

Status

approved