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A194768 Sum of distinct positive fifth powers.

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