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A252594
Records in A072994.
1
1, 2, 8, 16, 27, 32, 54, 64, 100, 128, 200, 243, 256, 400, 486, 500, 512, 800, 972, 1000, 1024, 1600, 1944, 2000, 2048, 3200, 3888, 4000, 4096, 4624, 6400, 7776, 8000, 8192, 9248, 12100, 12500, 12800, 15552, 16000, 16384, 18496, 24200, 25000, 25600, 31104, 32000, 32768, 36992, 48400, 50000
OFFSET
1,2
COMMENTS
Consider the function f(n) = the number of positive integers k < n such that k^n (mod n) == 1. This sequence lists the values of n at which f(n) reaches a new maximum.
All powers of two are present except its square. f(2^n) (with exception noted) = 2^(n-1) = 2^n/2.
All powers of two multiplied by 100, 1000 and 100000, but not 10000, are also present.
Terms other than the above are 27, 54, 243, 486, 500, 972, 1944, 3888, 4624, 7776, 9248, 12100, 12500, 15552, 18496, 24200, 25000, 31104, 36992, 48400, 50000, ..., .
Conjecture: f(x)/x -> 5/12.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..94
MATHEMATICA
f[n_] := (d = If[ OddQ@ n, 1, 2]; d*Length@ Select[ Range[ n/d], PowerMod[#, n, n] == 1 &]); f[1] = 1; k = 1; mx = 0; lst = {}; While[k < 10000001, a = f@ k; If[a > mx, mx = a; AppendTo[lst, k]; Print[{a, k}]]; k++]; lst
CROSSREFS
Cf. A072994.
Sequence in context: A225289 A322945 A157512 * A137882 A194643 A327329
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Dec 18 2014
STATUS
approved