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A082872 a^n + b^n + c^n + ..., where a*b*c* ... is the prime factorization of n.

%I A082872 #26 Dec 15 2017 17:36:11
%S A082872 1,4,27,32,3125,793,823543,768,39366,9766649,285311670611,539633,
%T A082872 302875106592253,678223089233,30531927032,262144,
%U A082872 827240261886336764177,775103122,1978419655660313589123979,95367433737777,558545874543637210
%N A082872 a^n + b^n + c^n + ..., where a*b*c* ... is the prime factorization of n.
%C A082872 n*log_10(2) + log_10(log_2(n)) <= length(a(n)) <= n*log_10(n). - Martin Renner, Jan 18 2012
%C A082872 If m = p^k is a power of a prime then a(n) = sum(p^m,i=1..k) = k*p^m is composite. - Martin Renner, Jan 31 2013
%H A082872 T. D. Noe, <a href="/A082872/b082872.txt">Table of n, a(n) for n = 1..100</a>
%e A082872 a(6) = a(2*3) = 2^6 + 3^6 = 793.
%e A082872 a(8) = a(2*2*2) = 2^8 + 2^8 + 2^8 = 768.
%p A082872 A082872 := proc(n)
%p A082872     local ps;
%p A082872     if n= 1 then
%p A082872         1;
%p A082872     else
%p A082872         ps := ifactors(n)[2] ;
%p A082872         add( op(2,p)*op(1,p)^n,p=ps) ;
%p A082872     end if;
%p A082872 end proc: # _R. J. Mathar_, Mar 12 2014
%t A082872 Table[f = FactorInteger[n]; Total[Flatten[Table[Table[f[[i, 1]], {f[[i, 2]]}], {i, Length[f]}]]^n], {n, 25}] (* _T. D. Noe_, Feb 01 2013 *)
%t A082872 Table[Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]^n],{n,30}] (* _Harvey P. Dale_, Jun 10 2016 *)
%Y A082872 Cf. A082813, A082814, A051674.
%K A082872 nonn,easy
%O A082872 1,2
%A A082872 _Jason Earls_, May 25 2003