A340325 - OEIS

%I #18 Feb 06 2021 12:35:37

%S 5,6,10,11,12,13,14,15,17,18,19,20,22,23,24,25,26,28,29,30,33,34,35,

%T 36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,

%U 59,60,61,62,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,82,83,84

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

%C From _Sebastian Karlsson_, Jan 15 2021: (Start)

%C 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:

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

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

%t fa[n_]:=fa[n]=FactorInteger[n];phi[1]=1; phi[p_, s_]:= (p + 1)*( p - 1)^(s - 1)

%t phi[n_]:=Product[phi[fa[n][[i, 1]], fa[n][[i, 2]]], {i, Length[fa[n]]}];

%t S[n_] := NestWhile [phi, n, ! ( # == 12 || # == 3 || # == 4) &];

%t Select[1 + Range[100], S[#] == 12 &]

%o (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

%o isok(m) = if (m==1, return(0)); while(! ((m==3) || (m==4) || (m==12)), m = f(m)); (m==12); \\ _Michel Marcus_, Jan 21 2021

%Y Cf. A340323, A340324.

%Y Cf. A000668.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Jan 07 2021