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%I #28 Jun 01 2022 17:45:46
%S 0,2,5,9,14,20,27,35,44,54,65,77,90,104,119,135,152,170,189,209,230,
%T 252,275,299,324,350,377,405,434,464,495,527,560,594,629,665,702,740,
%U 779,819,860,902,945,989,1034,1080,1127,1175,1224,1274,1325,1377,1430,1484
%N Sum of the integers from 1 to n, excluding the perfect sixth powers.
%H T. D. Noe, <a href="/A132337/b132337.txt">Table of n, a(n) for n = 1..10000</a>
%F Let r = floor(n^(1/6)). Then a(n) = n(n+1)/2 - (r^7/7 + r^6/2 + r^5/2 - r^3/6 + r/42) = A000217(n) - A000540(r).
%F a(n) = A000217(n) - A000540(A178489(n)). - _M. F. Hasler_, Oct 09 2010
%p A132337 := proc(n) r := floor(n^(1/6)) ; A000217(n)-A000540(r); end proc: seq(A132337(n),n=1..40) ; # _R. J. Mathar_
%t Accumulate[Table[If[IntegerQ[Surd[n,6]],0,n],{n,60}]] (* _Harvey P. Dale_, Jun 01 2022 *)
%o (PARI) g6(n)=for(x=1,n,r=floor(x^(1/6));sum6=r^7/7+r^6/2+r^5/2-r^3/6+r/ 42;sn=x* (x+1)/2;print1(sn-sum6","))
%o (PARI) A132337(n)=n*(n+1)/2-(1+n=floor(sqrtn(n+.5,6)))*(2*n+1)*((n^3+2*n^2-1)*n*3+1)*n/42 \\ _M. F. Hasler_, Oct 09 2010
%Y Different from A000096.
%Y Cf. A132336, A178489.
%K nonn,easy
%O 1,2
%A _Cino Hilliard_, Nov 07 2007
%E Incorrect formula deleted by _Jon E. Schoenfield_, Jun 12 2010
%E Incorrect program replaced by _R. J. Mathar_, Oct 08 2010
%E Edited by the Assoc. Editors of the OEIS, Oct 12 2010. Thanks to _Daniel Mondot_ for pointing out that the sequence needed editing.
%E Incorrect linear recurrence removed by _Georg Fischer_, Apr 11 2019
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