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%I #26 Mar 30 2024 07:33:36
%S 539633,
%T 43909277783870034878569768760415886733743786946105343887995366054267119200102384004474562849
%N Prime numbers of form a^m + b^m + c^m + ..., where a*b*c* ... is the prime factorization of m.
%C No more terms with m < 822. - _W. Edwin Clark_, May 24 2003
%C No more terms with m < 10000. - Joint effort of _Hugo Pfoertner_ and _Joshua Zucker_, May 30 2003
%C No more terms with m < 25500. - _Martin Renner_, Jan 31 2012
%H Hugo Pfoertner, <a href="/A082813/b082813.txt">Table of n, a(n) for n = 1..3</a>
%H G. L. Honaker, Jr., <a href="https://t5k.org/curios/page.php?short=539633">539633</a>
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a082813.zip">Program and input files for PFGW</a>.
%e a(1) = 539633 = 2^12 + 2^12 + 3^12 and 2*2*3 = 12.
%e a(2) is 2^88 + 2^88 + 2^88 + 11^88.
%e a(3) is 3^207 + 3^207 + 23^207.
%Y Cf. A082814 for values of m.
%K nonn,hard,bref
%O 1,1
%A _N. J. A. Sloane_, following a suggestion of _G. L. Honaker, Jr._, May 24 2003
%E a(2) and a(3) from _Joshua Zucker_, May 24 2003. Their primality was confirmed by _Hugo Pfoertner_, May 24 2003.
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