A082813, A082814

[all at abouthugo.de]

"N. J. A. Sloane" <njas at research.att.com> schrieb am 24.05.2003,
20:10:29:
> 
> Thanks to everyone who responded.  Here is the result:
> 
> %I A082813
> %S A082813 539633,
> %T A082813 43909277783870034878569768760415886733743786946105343887995366054267119200102384004474562849
> %N A082813 Prime numbers of form a^m + b^m + c^m + ... , where a*b*c* ... is the prime factorization of m.
> %H A082813 G. L. Honaker, Jr., 539633
> %O A082813 1,1
> %K A082813 nonn
> %Y A082813 Cf. A082814 for values of m.
> %e A082813 a(1) = 539633 = 2^12 + 2^12 + 3^12 and 2*2*3 = 12. a(2) is 2^88 + 2^88 + 2^88 + 11^88; a(3) is 3^207 + 3^207 + 23^207.
> %A A082813 njas, following a suggestion of G. L. Honaker, Jr., May 24 2003
> %E A082813 More terms from Joshua Zucker (joshua.zucker at stanfordalumni.org), May 24, 2003. Their primality was confirmed by Hugo Pfoertner (all(AT)abouthugo.de), May 24, 2003.
> 
> %I A082814
> %S A082814 12,88,207
> %N A082814 Values of m associated with A082813.
> %O A082814 1,1
> %K A082814 nonn,bref,more
> %Y A082814 Cf. A082813.
> %A A082814 njas, May 24 2003
> 
> NJAS

Neil, SeqFans,
the two sequences seem to offer rather
strong resistance against being extended.
I have now run
PFGW Version 20021101.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4]
from
http://www.primeform.net/openpfgw/
up to n=4000  and found no further terms.
Details can be found at
http://www.randomwalk.de/sequences/a082813.zip

The two sequences should be labeled "hard" ;-)

Hugo Pfoertner