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%I #16 May 08 2018 15:11:56
%S 42,101,6720,9212,226570,276404,288086,299668,339098,392228,412276,
%T 423395,530917,535759,559427,564209,666181,2835284,3592300,3911744,
%U 4080100,5980673,7230960,8787900,14960924,17130550,23324242,27449729,30437729,33869141,42073800
%N Numbers n such that phi(phi(n)) + sigma(sigma(n)) is an 8th power.
%D W. L. Glaisher, Number-Divisor Tables. British Assoc. Math. Tables, Vol. 8, Camb. Univ. Press, 1940, p. 64.
%D S. W. Golomb, Equality among number-theoretic functions, Abstract 882-11-16, Abstracts Amer. Math. Soc., 14 (1993), 415-416.
%D R. K. Guy, Unsolved Problems in Number Theory, B42.
%H Hiroaki Yamanouchi, <a href="/A172465/b172465.txt">Table of n, a(n) for n = 1..267</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H K. Ford, <a href="http://dx.doi.org/10.1090/S1079-6762-98-00043-2">The distribution of totients</a>, Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 27-34.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CarmichaelsTotientFunctionConjecture.html">Carmichael's Totient Function conjecture</a>
%e phi(phi(9)) + sigma(sigma(9))= 1;
%e phi(phi(42)) + sigma(sigma(42))= 2^8 = 256;
%e phi(phi(101)) + sigma(sigma(101))= 2^8 = 256;
%e phi(phi(6720)) + sigma(sigma(6720))= 4^8 = 65536.
%p with(numtheory):for n from 1 to 2000000 do;if floor(( phi(phi(n)) + sigma(sigma(n)))^.125) = (phi(phi(n)) + sigma(sigma(n)))^.125 then print (n);fi ; od;
%o (PARI) isok(n) = ispower(eulerphi(eulerphi(n)) + sigma(sigma(n)), 8); \\ _Michel Marcus_, Sep 20 2014
%Y Cf. A000010, A002180, A032446, A058277.
%K nonn
%O 1,1
%A _Michel Lagneau_, Feb 03 2010
%E a(10) corrected and a(18)-a(31) added by _Hiroaki Yamanouchi_, Sep 19 2014
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