A077090 When iteration of f(x) = phi(sigma(x) - phi(x)) is started at initial values listed here it ends up in a cycle of length greater than 1.
36, 40, 48, 50, 52, 60, 64, 66, 72, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 100, 102, 105, 106, 108, 110, 112, 114, 116, 117, 118, 120, 122, 123, 124, 126, 128, 130, 132, 135, 136, 138, 140, 141, 142, 144, 146, 147, 148, 150, 152, 154, 156, 159, 160, 162, 164
Offset: 1
Keywords
Examples
36 is in the sequence because f(36) = 78, f(78) = 48 and f(48) = 36, which is a cycle of length 3. 38 is not in the sequence because iterating f from 38 gives the trajectory 38, 12, 8, 10, 6, 4, 4, 4, ... where the cycle has a length of 1.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
f[x_] := EulerPhi[DivisorSigma[1, x] - EulerPhi[x]]; Do[s = NestList[f, n, 100]; s1 = Part[s, 98]; s2 = Part[s, 99]; s3 = Part[s, 100]; If[ !Equal[s1, s2], k = k + 1; Print[{k, n, s1, s2, s3}]], {n, 2, 1000}] f[n_] := EulerPhi[DivisorSigma[1, n]-EulerPhi[n]]; cycleQ[n_] := With[{nn = NestWhileList[f, n, Unequal, All]}, nn[[-1]] != nn[[-2]]]; Select[Range[200], cycleQ] (* Jean-François Alcover, Nov 29 2013 *) -
PARI
f(x)=if(x>35,eulerphi(sigma(x)-eulerphi(x)),1) is(n)=my(t=f(n),h=f(t)); while(t!=h, h=f(f(h)); t=f(t)); f(t)!=t \\ Charles R Greathouse IV, Nov 29 2013
Extensions
Name corrected by Charles R Greathouse IV, Nov 29 2013
Comments