This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A077090 #30 May 07 2025 05:29:38
%S A077090 36,40,48,50,52,60,64,66,72,76,78,80,81,84,88,90,92,96,98,100,102,105,
%T A077090 106,108,110,112,114,116,117,118,120,122,123,124,126,128,130,132,135,
%U A077090 136,138,140,141,142,144,146,147,148,150,152,154,156,159,160,162,164
%N 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.
%C A077090 Below 2000 there are only these two cycles of length 3: 36, 78, 48; and 144, 280, 192.
%C A077090 For most composite numbers below 80, the iterated trajectory of f settles on a single-number cycle of 4; those numbers are not in this sequence. - _Alonso del Arte_, Nov 29 2013
%H A077090 Charles R Greathouse IV, <a href="/A077090/b077090.txt">Table of n, a(n) for n = 1..10000</a>
%e A077090 36 is in the sequence because f(36) = 78, f(78) = 48 and f(48) = 36, which is a cycle of length 3.
%e A077090 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.
%t A077090 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}]
%t A077090 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 *)
%o A077090 (PARI) f(x)=if(x>35,eulerphi(sigma(x)-eulerphi(x)),1)
%o A077090 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
%Y A077090 Cf. A077088, A077091, A077092, A077093, A077094, A077095, A077096.
%K A077090 nonn
%O A077090 1,1
%A A077090 _Labos Elemer_, Oct 31 2002
%E A077090 Name corrected by _Charles R Greathouse IV_, Nov 29 2013