A132337 Sum of the integers from 1 to n, excluding the perfect sixth powers.

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

Offset: 1

Author

Cino Hilliard, Nov 07 2007

Keywords

• nonn
• easy

Links

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

Crossrefs

Different from A000096.

Cf. A132336, A178489.

Programs

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 *)

PARI

g6(n)=for(x=1,n,r=floor(x^(1/6));sum6=r^7/7+r^6/2+r^5/2-r^3/6+r/ 42;sn=x* (x+1)/2;print1(sn-sum6","))

PARI

A132337(n)=n*(n+1)/2-(1+n=floor(sqrtn(n+.5,6)))*(2*n+1)*((n^3+2*n^2-1)*n*3+1)*n/42 \\ M. F. Hasler, Oct 09 2010

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

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