%I #21 Aug 02 2023 06:07:05
%S 1,32,33,243,244,275,276,1024,1025,1056,1057,1267,1268,1299,1300,3125,
%T 3126,3157,3158,3368,3369,3400,3401,4149,4150,4181,4182,4392,4393,
%U 4424,4425,7776,7777,7808,7809,8019,8020,8051,8052,8800,8801,8832,8833,9043,9044,9075,9076
%N Sum of distinct positive fifth powers.
%C From _Peter Munn_, Aug 02 2023: (Start)
%C 67898771 = A001661(5) is the largest number not in the sequence.
%C After a(1) = 1, the next term that is in all the analogous sequences for smaller powers is a(35) = 7809 = A364637(5).
%C If we tightened the sequence requirement so that the sum was of more than one 5th power, we would remove exactly 24 5th powers from the terms: row 5 of A332065 indicates which 5th powers would remain.
%C (End)
%H Robert Israel, <a href="/A194768/b194768.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F For n > 53986089, a(n) = n + 13912682. [_Charles R Greathouse IV_, Sep 02 2011]
%p N:= 2*10^4: # to get all terms <= N
%p S:= {0}:
%p for i from 1 while i^5 <= N do
%p S:= select(`<=`, map(`+`,S,i^5),N) union S
%p od:
%p sort(convert(S minus {0},list)); # _Robert Israel_, Jun 26 2019
%o (PARI) upto(lim)={
%o lim\=1;
%o my(v=List(),P=prod(n=1,lim^(1/5),1+x^(n^5),1+O(x^(lim+1))));
%o for(n=1,lim,if(polcoeff(P,n),listput(v,n)));
%o Vec(v)
%o }; \\ _Charles R Greathouse IV_, Sep 02 2011
%Y Cf. A000584 (5th powers), A001661, A332065, A364637.
%Y Cf. A003997, A003999, A194769 (analogs for 3rd, 4th and 6th powers).
%Y A217845 is a subsequence.
%K nonn
%O 1,2
%A _Charles R Greathouse IV_, Sep 02 2011
%E Name qualified by _Peter Munn_, Aug 02 2023