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Search: id:A160599
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| A160599 |
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Composite numbers n for which n-eulerphi(n) divides n-1. |
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+0
2
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| 15, 85, 255, 259, 391, 589, 1111, 3193, 4171, 4369, 12361, 17473, 21845, 25429, 28243, 47989, 52537, 65535, 65641, 68377, 83767, 91759, 100777, 120019, 144097, 167743, 186367, 268321, 286357, 291919, 316171, 327937, 335923, 346063, 353029
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Obviously C(p)=(p-eulerphi(p))/(p-1) = 1/(p-1), i.e. A160598(p)=1, for all primes p. This sequence lists composite numbers for which C(n) has denominator 1, i.e. n-1 is a multiple of n-eulerphi(n).
The sequence contains numbers F(k)*F(k+1)*...*F(k+d), if the factors are successive Fermat primes F(k)=2^(2^k)+1.
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LINKS
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Project Euler, Problem 245: resilient fractions, May 2009
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EXAMPLE
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a(1)=15 is in the sequence, because for n=15, we have (n-eulerphi(n))/(n-1) = (15-8)/14 = 1/2; Apart from the primes, this is the smallest number such that C(n) is a unit fraction.
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PROGRAM
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(PARI) for(n=2, 10^9, isprime(n) & next; (n-1)%(n-eulerphi(n)) | print1(n", "))
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CROSSREFS
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Cf. A160597-A160598.
Sequence in context: A050405 A020136 A067401 this_sequence A091286 A064058 A138322
Adjacent sequences: A160596 A160597 A160598 this_sequence A160600 A160601 A160602
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), May 23 2009
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