A376256 - OEIS

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

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OFFSET

1,2

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

Table of n, a(n) for n=1..42.

Richard R. Forberg, Prevalence of Cycles vs. "Unruly Events" from 10^8 to 10^55 after Iterating on phi(sigma(n)<-n

Richard R. Forberg, 422 Phi Sigma Cycles Organized by Length

PROG

(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

CROSSREFS

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

Cf. A062401, A095955.

Sequence in context: A368507 A273109 A046843 * A373728 A292060 A152125

Adjacent sequences: A376253 A376254 A376255 * A376257 A376258 A376259

KEYWORD

nonn,changed

AUTHOR

Richard R. Forberg, Sep 16 2024

STATUS

approved