A340325 Numbers k such that starting with k and repeatedly applying the map x -> A340323(x) reaches the fixed point 12.

5, 6, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84

Offset: 1

Author

José María Grau Ribas, Jan 07 2021

Keywords

• nonn

Comments

From Sebastian Karlsson, Jan 15 2021: (Start)

The sequence contains no powers of two. If a number isn't a power of two, then it is in this sequence if and only if either of the following conditions hold:

- It is a multiple of a prime that is not a Mersenne prime.

- It is divisible by the square of a Mersenne prime greater than 3. (End)

Crossrefs

Cf. A340323, A340324.

Cf. A000668.

Programs

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], S[#] == 12 &]

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==12); \\ Michel Marcus, Jan 21 2021