# [seqfan] Re: trouble with A132337 and A132336

Richard Mathar mathar at strw.leidenuniv.nl
Fri Oct 8 22:45:03 CEST 2010

```A132336 should perhaps have a clearer  definition, formula, program example etc,
but I don't see any actual error in there:

%I A132336
%S A132336 0,2,5,9,14,20,27,35,44,54,65,77,90,104,119,135,152,170,189,209,230,252,
%T A132336 275,299,324,350,377,405,434,464,495,495,528,562,597,633,670,708,747,
%U A132336 787,828,870,913,957,1002,1048,1095,1143,1192,1242,1293,1345,1398,1452
%N A132336 Sum of the integers from 0 to n, excluding perfect fifth powers.
%F A132336 a(n) = A000217(n) -A000539(r) where r = floor(n^(1/5)).
%F A132336 a(n) = n(n+1)/2 - (2r^6+6r^5+5r^4-r^2)/12.
%e A132336 a(1)=0+1, excluding 0 and 1, so a(1)=0. a(2)=0+1+2, excluding 0 and 1, so a(2)=2.
%e A132336 a(3)=0+1+2+3, excluding 0 and 1, so a(3)=2+3=5.
%p A132336 A000217 := proc(n) n*(n+1)/2 ; end proc:
%p A132336 A000539 := proc(n) (2*n^6+6*n^5+5*n^4-n^2)/12 ; end proc:
%p A132336 A132336 := proc(n) r := floor(n^(1/5)) ; A000217(n)-A000539(r); end proc: seq(A132336(n),n=1..40) ;
%o A132336 (PARI) g5(n)=for(x=1,n,r=floor(x^(1/5));sum5=(2*r^6+6*r^5+5*r^4-r^2)/ 12;sn=x* (x+1)/2;print1(sn-sum5","))
%Y A132336 Different from A000096.
%Y A132336 Adjacent sequences: A132333 A132334 A132335 this_sequence A132337 A132338 A132339
%Y A132336 Sequence in context: A112265 A075543 A132315 this_sequence A000096 A080956 A132337
%K A132336 nonn
%O A132336 1,2
%A A132336 Cino Hilliard (hillcino368(AT)hotmail.com), Nov 07 2007

```