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A125774
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Numbers n such that 3^n (mod n) = 3^n (mod n^2).
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2
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1, 2, 3, 4, 9, 11, 20, 22, 27, 33, 81, 99, 220, 243, 644, 729, 1220, 2187, 2420, 5060, 6561, 7128, 8368, 13420, 14740, 19683, 23620, 40573, 55660, 59049, 145420, 147620, 162140, 177147, 237820, 259820, 290620, 308660, 339020, 447740, 531441, 548660
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) includes all powers of 3. a(2) = 2, a(3) = 3, a(6) = 11 and a(45) = 1006003 are the only known primes in a(n).
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MATHEMATICA
| Do[f=PowerMod[3, n, n]; g=PowerMod[3, n, n^2]; If[f==g, Print[n]], {n, 1, 1100000}]
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CROSSREFS
| Cf. A014127 = Primes p such that p^2 divides 3^(p-1) - 1. Cf. A068535 = numbers n such that 2^n (mod n) = 2^n (mod n^2). Cf. A125773 = numbers n, that are not the powers of 2, such that 2^n (mod n) = 2^n (mod n^2). Cf. A125775 = numbers n such that 5^n (mod n) = 5^n (mod n^2).
Sequence in context: A118223 A093514 A080231 * A062410 A145772 A027866
Adjacent sequences: A125771 A125772 A125773 * A125775 A125776 A125777
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 07 2006
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