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A132336
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Sum of the integers from 1 to n, excluding perfect fifth powers.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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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). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 12 2010]
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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.
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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) ;
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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", "))
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CROSSREFS
| Different from A000096.
Cf. A132337.
Sequence in context: A112265 A075543 A132315 * A080956 A000096 A132337
Adjacent sequences: A132333 A132334 A132335 * A132337 A132338 A132339
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Nov 07 2007
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EXTENSIONS
| Edited by the Assoc. Editors of the OEIS, Oct 12 2010. Thanks to Daniel Mondot for pointing out that the sequence needed editing.
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