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

1,1

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)

Links

Table of n, a(n) for n=1..69.

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 &]

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

Crossrefs

Cf. A340323, A340324.

Cf. A000668.

Sequence in context: A019205 A191472 A189056 * A247561 A273401 A042958

Adjacent sequences: A340322 A340323 A340324 * A340326 A340327 A340328

Keyword

nonn

Author

José María Grau Ribas, Jan 07 2021

Status

approved