[seqfan] Re: trouble with A132337 and A132336

[Alonso Del Arte]

At least for A132337, the line

"Let r = floor(n^(1/6)). Then a(n) = n(n+1)/2 -
(n^7/7+n^6/2+n^5/2-n^3/6+n/42)."

needs to be changed to

"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)."

because otherwise the definition of r is just there as a useless ornament.

In Mathematica,

Table[n (n + 1)/2 - ((Floor[n^(1/6)])^7/7 + (Floor[n^(1/6)])^6/2 +
(Floor[n^(1/6)])^5/2 - (Floor[n^(1/6)])^3/6 + (Floor[n^(1/6)])/42), {n, 54}]
== A132337

gives True (with A132337 being copied and pasted from the OEIS as it stands
now).

I have also confirmed that this sequence differs from A000096 beyond term
visibility.
And I also had Mathematica compute the sequence by testing each number for
sixth powerness:

f[n_]:=Plus@@Table[Boole[m^(1/6)-Floor[m^(1/6)]!=0]*m,{m,n}]

Table[f[n],{n,54}]

This also matches A132337.

I haven't looked at A132336 but I suspect that there is a simple typo that
needs correction there as well.

Al

On Fri, Oct 8, 2010 at 4:15 PM, N. J. A. Sloane <njas at research.att.com>wrote:

> A sixth power is a number n = m^6 for some m
>
> (your 5th definition)
>
>
>  Best regards
>                          Neil
>
>
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