A376256 Numbers which are the minimum of a cycle in the map x -> phi(sigma(x)).

1, 2, 4, 8, 12, 16, 48, 72, 128, 240, 432, 576, 720, 1200, 1728, 1800, 6912, 10368, 15552, 27648, 32768, 41472, 67392, 142560, 184320, 272160, 326592, 712800, 1140480, 1190400, 1658880, 3345408, 3571200, 5702400, 6220800, 10222080, 14859936, 29719872, 40255488, 50319360, 113218560, 118879488

Offset: 1

Author

Richard R. Forberg, Sep 16 2024

Keywords

• nonn

Comments

No further terms < 254731536.

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

Additional terms include 2142720000, 5033164800, 150493593600, 3852635996160.

See further cycles in the linked document here below which contains 422 cycles. It includes the 80 cycles complied by Jud McCrainie in a linked document at A095955.

Links

• Richard R. Forberg, The Prevalence of Cycles vs. "Unruly Events" from 10^8 to 10^55 after Iterating on n <- phi(sigma(n))
• Richard R. Forberg, 422 Phi Sigma Cycles Organized by Length

Crossrefs

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

Cf. A062401, A095955.

Programs

PARI

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