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%I #52 Dec 10 2020 17:36:44
%S 1,2,8,12,128,240,720,6912,32768,142560,712800,1140480,1190400,
%T 3345408,3571200,5702400,14859936,29719872,50319360,118879488,
%U 2147483648,3889036800,4389396480,21946982400,47416320000,92177326080,133145026560,331914240000
%N Numbers n such that phi(sigma(n)) = n.
%C For n=0,1,2,3,4 & 5 2^(2^n-1) is in the sequence because 2^2^n+1 is prime for n=0,1,2,3 & 4 (Fermat primes). - _Farideh Firoozbakht_, Oct 08 2004
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 128, p. 44, Ellipses, Paris 2008.
%D J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 702 pp. 92; 300-1, Ellipses Paris 2004.
%D R. K. Guy, Unsolved Problems in Number Theory, B42.
%H Leon Alaoglu and Paul Erdős, <a href="http://www.renyi.hu/~p_erdos/1944-01.pdf">A conjecture in elementary number theory</a>, Bull. Amer. Math. Soc. 50 (1944), pp. 881-882.
%H Graeme L. Cohen, <a href="http://matwbn.icm.edu.pl/ksiazki/cm/cm74/cm7411.pdf">On a conjecture of Makowski and Schinzel</a>, Colloquium Mathematicae, Vol. 74, No. 1 (1997), pp. 1-8. See Notes p. 7.
%H Fred W. Helenius, <a href="http://www.netcom.com/~fredh/phisigma/pslist.html">664 solutions</a> [Broken Link]
%H Fred W. Helenius, <a href="https://web.archive.org/web/20171109072644/http://pweb.netcom.com/~fredh/phisigma/pslist.html">664 solutions</a> [From the Wayback machine]
%H T. Negadi, <a href="http://arxiv.org/abs/1406.6092">The genetic code invariance: when Euler and Fibonacci meet</a>, arXiv preprint arXiv:1406.6092 [q-bio.OT], 2014; Symmetry: Culture and Science, Vol. 25, No. 3, 261-278, 2014.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function.</a>
%F phi(A018784), sorted. - _David W. Wilson_, Oct 18 2012
%t Select[Range[10000], EulerPhi[DivisorSigma[1, #]] == # &] (* _T. D. Noe_, Jun 26 2012 *)
%o (PARI) is(n)=eulerphi(sigma(n))==n \\ _Charles R Greathouse IV_, May 15 2013
%Y Cf. A000010, A018784, A135240.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_, Aug 15 1996 (search was complete only through a(19) = 50319360).
%E _Jud McCranie_ reports Jun 15 1998 that the terms through a(24) are certain.
%E a(28) added. Verified sequence is complete through a(28) by _Donovan Johnson_, Jun 30 2012
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