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A194769 Sum of distinct nonzero sixth powers.

%I A194769 #32 Aug 02 2023 06:09:01
%S A194769 1,64,65,729,730,793,794,4096,4097,4160,4161,4825,4826,4889,4890,
%T A194769 15625,15626,15689,15690,16354,16355,16418,16419,19721,19722,19785,
%U A194769 19786,20450,20451,20514,20515,46656,46657,46720,46721,47385,47386,47449,47450,50752,50753,50816
%N A194769 Sum of distinct nonzero sixth powers.
%C A194769 See A001661 for a proof of the formula. - _M. F. Hasler_, May 15 2020
%C A194769 From _Peter Munn_, Aug 02 2023: (Start)
%C A194769 11146309947 = A001661(6) is the largest number not in the sequence.
%C A194769 After a(1) = 1, the next term that is in all the analogous sequences for smaller powers is a(86) = 134067 = A364637(6).
%C A194769 If we tightened the sequence requirement so that the sum was of more than one 6th power, we would remove exactly 30 6th powers from the terms: row 6 of A332065 indicates which 6th powers would remain.
%C A194769 (End)
%H A194769 David A. Corneth, <a href="/A194769/b194769.txt">Table of n, a(n) for n = 1..10000</a>
%H A194769 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A194769 For n > 9108736851, a(n) = n + 2037573096.
%o A194769 (PARI) upto(lim)={
%o A194769     lim\=1;
%o A194769     my(v=List(),P=prod(n=1,lim^(1/6),1+x^(n^6),1+O(x^(lim+1))));
%o A194769     for(n=1,lim,if(polcoeff(P,n),listput(v,n)));
%o A194769     Vec(v)
%o A194769 }
%Y A194769 Cf. A001014, A001661, A332065, A364637.
%Y A194769 A217846 is a subsequence.
%Y A194769 Cf. A003997, A003999, A194768 (analogs for 3rd, 4th and 5th powers).
%K A194769 nonn,easy
%O A194769 1,2
%A A194769 _Charles R Greathouse IV_, Sep 02 2011
%E A194769 More terms from _David A. Corneth_, Apr 21 2020
%E A194769 Name qualified by _Peter Munn_, Aug 02 2023