A132336 Sum of the integers from 1 to n, excluding perfect fifth 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, 495, 528, 562, 597, 633, 670, 708, 747, 787, 828, 870, 913, 957, 1002, 1048, 1095, 1143, 1192, 1242, 1293, 1345, 1398, 1452

Offset

1,2

Links

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

Formula

a(n) = A000217(n) - A000539(r) where r = floor(n^(1/5)).

a(n) = n(n+1)/2 - (2r^6 + 6r^5 + 5r^4 - r^2)/12.

a(n) = A000217(n) - A000539(r) where r= A178487(n). - R. J. Mathar, Oct 12 2010

Example

a(1)=0+1, excluding 0 and 1, so a(1)=0.
a(2)=0+1+2, excluding 0 and 1, so a(2)=2.
a(3)=0+1+2+3, excluding 0 and 1, so a(3)=2+3=5.

Maple

A000217 := proc(n) n*(n+1)/2 ; end proc:
A000539 := proc(n) (2*n^6+6*n^5+5*n^4-n^2)/12 ; end proc:
A132336 := proc(n) r := floor(n^(1/5)) ; A000217(n)-A000539(r); end proc: seq(A132336(n), n=1..40) ;

Prog

(PARI) g5(n)=for(x=1, n, r=floor(x^(1/5)); sum5=(2*r^6+6*r^5+5*r^4-r^2)/12; sn=x* (x+1)/2; print1(sn-sum5, ", "))
(PARI) a(n) = my(r=sqrtnint(n, 5)); n*(n+1)/2 - (2*r^6+6*r^5+5*r^4-r^2)/12; \\ Ruud H.G. van Tol, Nov 02 2023

Crossrefs

Cf. A000217, A000539, A178487.

Different from A000096.

Cf. A132337.

Sequence in context: A075543 A132315 A079509 * A272370 A212342 A080956

Adjacent sequences: A132333 A132334 A132335 * A132337 A132338 A132339

Keyword

nonn,easy

Author

Cino Hilliard, Nov 07 2007

Extensions

Edited by the Assoc. Editors of the OEIS, Oct 12 2010. Thanks to Daniel Mondot for pointing out that the sequence needed editing.

Status

approved