

A132337


Sum of the integers from 1 to n, excluding the perfect sixth powers.


4



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
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OFFSET

1,2


LINKS



FORMULA

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).


MAPLE



MATHEMATICA

Accumulate[Table[If[IntegerQ[Surd[n, 6]], 0, n], {n, 60}]] (* Harvey P. Dale, Jun 01 2022 *)


PROG

(PARI) g6(n)=for(x=1, n, r=floor(x^(1/6)); sum6=r^7/7+r^6/2+r^5/2r^3/6+r/ 42; sn=x* (x+1)/2; print1(snsum6", "))
(PARI) A132337(n)=n*(n+1)/2(1+n=floor(sqrtn(n+.5, 6)))*(2*n+1)*((n^3+2*n^21)*n*3+1)*n/42 \\ M. F. Hasler, Oct 09 2010


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS

Edited by the Assoc. Editors of the OEIS, Oct 12 2010. Thanks to Daniel Mondot for pointing out that the sequence needed editing.
Incorrect linear recurrence removed by Georg Fischer, Apr 11 2019


STATUS

approved



