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Odd solutions of phi(sigma(n)) = sigma(phi(n)).
0

%I #7 Mar 05 2015 14:44:38

%S 9,225,729,18225,65025,140625,531441,5267025,11390625,13286025,

%T 18792225,40640625,87890625,1522170225,2197265625,3291890625,

%U 3839661225,5430953025,7119140625,8303765625,11745140625,25400390625

%N Odd solutions of phi(sigma(n)) = sigma(phi(n)).

%C sigma is the multiplicative sum-of-divisors function.

%C phi is Euler's totient.

%C Complete through 25558816403.

%C All given here are products of powers of consecutive Fermat primes based on generalized repunit primes; see links.

%C It is conjectured (see links) that all odd solutions are of this form, for which at least 10130 solutions are known.

%D Richard Guy, "Unsolved Problems in Number Theory", section B42

%D Oystein Ore, "Number Theory and Its History", 1948, reprinted 1988, Dover, ISBN-10: 0486656209, pp. 88 et seq., 109 et seq.

%H Walter Nissen, <a href="http://upforthecount.com/math/sigmaphi.html"> phi(sigma(n)) = sigma(phi(n))</a>

%e sigma(9) = 13, phi(9) = 6, sigma(6) = phi(13) = 12, so 9 is in the sequence.

%o (PARI) isok(n) = (n % 2) && (eulerphi(sigma(n)) == sigma(eulerphi(n))) \\ _Michel Marcus_, Jul 23 2013

%Y Cf. A000203, A000010, A033632, A019434.

%K nonn

%O 1,1

%A _Walter Nissen_, Apr 26 2009

%E Edited by _Charles R Greathouse IV_, Oct 28 2009