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%I #5 Jun 13 2016 08:31:37
%S 32,64,96,128,160,192,224,243,256,275,288,307,320,339,352,371,384,403,
%T 416,435,448,467,480,486,499,512,518,531,544,550,563,576,582,595,608,
%U 614,627,640,646,659,672,678,691,704,710,723,729,736,742,755,761,768
%N Sums of 5th powers of primes.
%C After a finite number of integers which cannot be written as a sum of 5th powers of primes, all integers can be so written.
%H Giovanni Resta, <a href="/A122616/b122616.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = a*32 + b*243 + c*3125 + d*16807 + e*161051 + ... where a,b,c,d,e,... are nonnegative integers. Sumset of A050997 Fifth powers of primes.
%t ok[n_] := {} != Quiet@ IntegerPartitions[n, All, Prime[ Range@ PrimePi@ Max[2, n^(1/5)]]^5, 1]; Select[Range[768], ok] (* _Giovanni Resta_, Jun 12 2016 *)
%Y Cf. A000040, A050997.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 21 2006
%E Several missing terms from _Giovanni Resta_, Jun 12 2016
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