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A132336
Sum of the integers from 1 to n, excluding perfect fifth powers.
2
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
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
Different from A000096.
Cf. A132337.
Sequence in context: A075543 A132315 A079509 * A272370 A212342 A080956
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