[seqfan] trouble with A132337 and A132336
N. J. A. Sloane
njas at research.att.com
Fri Oct 8 21:10:02 CEST 2010
Dear SeqFans, I received some emails from Daniel Mondot <dmondot at gmail.com>
who has been looking at A132337. He says:
(Start)
If the intent of A132337 is really
"a(n) is the sum of all numbers from 0 to n not counting the n's that
are a 6th power" then the series should be:
0, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170,
189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527,
560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, 989, 1034, 1080,
1127, 1175, 1224, 1274, 1325, 1377, 1430, 1484, 1539, 1595, 1652, 1710,
1769, 1829, 1890, 1952, 2015, 2015, 2080, 2146, 2213, 2281, 2350, 2420,
2491, 2563, 2636, 2710, 2785, 2861, 2938, 3016, 3095, 3175, 3256, 3338,
3421, 3505, 3590, 3676, 3763, 3851, 3940, 4030, 4121, 4213, 4306, 4400,
4495, 4591, 4688, 4786, 4885
basically elements 63 and 64 are the same, elements 728 & 729 are the
same.. etc...
and the formula:
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).=20
is completely wrong.
At the minimum, there should be a note that the first differing member
from A000096 is the 64th member.
Looking now at A132336 (Sum of the non-fifth powers less than or equal to n. )
The list of numbers is correct, but
the formula given for A132336, i.e. (Let r = floor(n^(1/5)).
Then a(n) = n(n+1)/2 - (2r^6+6r^5+5r^4-r^2)/12. )
is also incorrect.
(End)
Could some sequence fan confirm this? Thanks. Neil
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