

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

T. D. Noe, Table of n, a(n) for n = 1..10000


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).
a(n) = A000217(n)  A000540(A178489(n)).  M. F. Hasler, Oct 09 2010


MAPLE

A132337 := proc(n) r := floor(n^(1/6)) ; A000217(n)A000540(r); end proc: seq(A132337(n), n=1..40) ; # R. J. Mathar


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

Different from A000096.
Cf. A132336, A178489.
Sequence in context: A272370 A212342 A080956 * A000096 A134189 A109470
Adjacent sequences: A132334 A132335 A132336 * A132338 A132339 A132340


KEYWORD

nonn,easy


AUTHOR

Cino Hilliard, Nov 07 2007


EXTENSIONS

Incorrect formula deleted by Jon E. Schoenfield, Jun 12 2010
Incorrect program replaced by R. J. Mathar, Oct 08 2010
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



