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Numbers which are the minimum of a cycle in the map x -> phi(sigma(x)).
1

%I #53 Oct 15 2024 15:45:21

%S 1,2,4,8,12,16,48,72,128,240,432,576,720,1200,1728,1800,6912,10368,

%T 15552,27648,32768,41472,67392,142560,184320,272160,326592,712800,

%U 1140480,1190400,1658880,3345408,3571200,5702400,6220800,10222080,14859936,29719872,40255488,50319360,113218560,118879488

%N Numbers which are the minimum of a cycle in the map x -> phi(sigma(x)).

%C No further terms < 254731536.

%C The status of 254731536 is unknown, but conjectured not a term.

%C Additional terms include 2142720000, 5033164800, 150493593600, 3852635996160.

%C See further cycles in the linked document here below which contains 271 cycles, in Appendix C. It includes the 80 cycles complied by Jud McCrainie in a linked document at A095955.

%H Richard R. Forberg, <a href="/A376256/a376256.pdf">Collecting Meta-Data About phi(sigma(n)) Cycles and Finding Many More Cycles</a>, Oct 14, 2024.

%o (PARI) \\ Naive program, assumes eventual termination (ok upto 254731535).

%o isok(n)={my(M=Map(),p=n); while(!mapisdefined(M,p) && p>=n, mapput(M,p,1); p=eulerphi(sigma(p))); p==n} \\ _Andrew Howroyd_, Sep 19 2024

%Y Union of A001229, A373435, A373453, A373454, etc.

%Y Cf. A062401, A095955.

%K nonn

%O 1,2

%A _Richard R. Forberg_, Sep 16 2024