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A159939
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Odd solutions of phi ( sigma ( n ) ) = sigma ( phi ( n ) )
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0
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9, 225, 729, 18225, 65025, 140625, 531441, 5267025, 11390625, 13286025, 18792225, 40640625, 87890625, 1522170225, 2197265625, 3291890625, 3839661225, 5430953025, 7119140625, 8303765625, 11745140625, 25400390625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| sigma is the multiplicative sum-of-divisors function.
phi is Euler's totient.
Complete through 25558816403 .
All given here are products of powers of consecutive Fermat primes based on generalized repunit primes; see links.
It is conjectured (see links) that all odd solutions are of this form, for which at least 10130 solutions are known.
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REFERENCES
| Richard Guy, "Unsolved Problems in Number Theory", section B42
Oystein Ore, "Number Theory and Its History", 1948, reprinted 1988, Dover, ISBN-10: 0486656209, pp. 88 et seq., 109 et seq.
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LINKS
| Walter Nissen, Home Page (listed in lieu of email address)
Walter Nissen, phi ( sigma ( n ) ) = sigma ( phi ( n ) )
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EXAMPLE
| sigma(9) = 13, phi(9) = 6, sigma(6) = phi(13) = 12, so 9 is in the sequence.
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CROSSREFS
| Cf. A000203, A000010, A033632, A019434.
Sequence in context: A057530 A014736 A017558 * A167038 A074190 A069075
Adjacent sequences: A159936 A159937 A159938 * A159940 A159941 A159942
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KEYWORD
| nonn
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AUTHOR
| Walter Nissen Apr 26 2009
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EXTENSIONS
| Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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