A096990 Initial values for f(x)=sigma(phi(x))=A062402(x) such that iteration of f ends in cycle of length=3.

17, 19, 27, 29, 31, 32, 34, 35, 38, 39, 40, 41, 45, 47, 48, 52, 54, 55, 56, 58, 59, 60, 62, 69, 70, 72, 75, 78, 82, 84, 88, 90, 92, 94, 100, 110, 118, 132, 138, 150, 1057, 1117, 1153, 1201, 1237, 1241, 1261, 1271, 1301, 1313, 1321, 1333, 1349, 1351, 1359, 1381

Offset: 1

Author

Labos Elemer, Jul 19 2004

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A062402, A095953.

Programs

Maple

kT:= {}: kF:= {}:
f:= proc(t) uses numtheory; local S,R,i,val,s; global kT, kF;
  if member(t,kT) then return true elif member(t,kF) then return false fi;
  R[0]:= t;
  S:= {t};
  for i from 1 do
    R[i]:= sigma(phi(R[i-1]));
    if member(R[i], kT) then val:= true
    elif member(R[i], kF) then val:= false
    elif member(R[i],S) then
      val:= evalb(R[i-3] = R[i]) and not member(R[i],[R[i-1],R[i-2]])
    else val:= fail; S:= S union {R[i]}
    fi;
    if val = true then kT:= kT union {R[i]} union S; return true
    elif val = false then kF:= kF union {R[i]} union S; return false
    fi
  od;
end proc:
select(f, [$1..3000]); # Robert Israel, Jun 09 2024

Mathematica

f[n_] := DivisorSigma[1, EulerPhi[n]]; g[n_] := Block[{l = NestWhileList[f, n, UnsameQ, All]}, -Subtract @@ Flatten[ Position[l, l[[ -1]]]]]; Select[ Range[ 1396], g[ # ] == 3 &] (* Robert G. Wilson v, Jul 23 2004 *)

Extensions

Edited and extended by Robert G. Wilson v, Jul 23 2004