A077082 -id:A077082 - cp's OEIS frontend

A077085 Initial values such that if A077080(x)=phi(sigma(x)+phi(x)) is started at these numbers then the sequence does not converge.

534, 556, 557, 580, 624, 702, 710, 738, 739, 740, 748, 784, 789, 822, 823, 841, 852, 853, 900, 912, 913, 916, 924, 931, 938, 960, 961, 962, 1020, 1021, 1029, 1032, 1033, 1034, 1065, 1089, 1092, 1093, 1098, 1126, 1136

Offset: 1

Labos Elemer, Oct 28 2002

nonn

These terms are only conjectures.

These terms survive 1000 iterations. - Sean A. Irvine, May 05 2025

Cf. A000010, A000203, A065387, A077080, A077081, A077082, A077083, A077084.

f[x_] := EulerPhi[DivisorSigma[1, x]+EulerPhi[x]] Do[s=Part[NestList[f, n, 100], 100]; If[Greater[s, 10000000], Print[{n, s}]], {n, 1, 10000}]

A077081 Fixed point when phi(sigma(n)+phi(n))=A077080 is iterated with initial value of n.

Original entry on oeis.org

1, 2, 2, 6, 6, 6, 6, 864, 864, 10, 10, 864, 864, 864, 864, 864, 864, 864, 864, 20, 20, 22, 22, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 48, 864, 46, 46, 48, 864, 864, 48, 864, 864, 48, 48, 48, 48, 58, 58

Offset: 1

Labos Elemer, Oct 28 2002

nonn

A065387 when iterated seems to converge [tested for initial values below 1024]. On the other hand iterating A051682 often ends in cycle.
Iteration of phi(A065387())=phi(sigma()+phi()) seems to converge. Tested below n=1024. Critical values however arise. For example: n=534,556,557,580,624,702,710, etc. These initial values generate very large terms and i was unable to decide if they converge.
For n=1..1024 no more but 27 distinct fixed points arised:{1,2,6,10,..,3552,570240}

			n=225: results in iteration sequence of 44 terms: {225,522,444,...,471744,653312,570240}, a[25]=570240.

Cf. A000010, A000203, A065387, A077080, A077082, A077083, A077084, A077085.

f[x_] := EulerPhi[DivisorSigma[1, x]+EulerPhi[x]] Table[FixedPoint[f, w], {w, 1, 256}]

a(n) = FixedPoint[A077080, n].

cp's OEIS Frontend

A077085 Initial values such that if A077080(x)=phi(sigma(x)+phi(x)) is started at these numbers then the sequence does not converge.

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