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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
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = n(n+1)/2 - (2r^6 + 6r^5 + 5r^4 - r^2)/12.
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EXAMPLE
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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
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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:
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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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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STATUS
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approved
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