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Search: id:A132337
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| A132337 |
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Sum of the non-sixth powers less than or equal to n. |
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+0
1
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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, 527, 560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, 989, 1034, 1080, 1127, 1175, 1224, 1274, 1325, 1377, 1430, 1484
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Let r = floor(n^(1/6)). Then a(n) = n(n+1)/2 - (n^7/7+n^6/2+n^5/2-n^3/6+n/42).
a(n)=n+a(n-1) (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 18 2009]
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EXAMPLE
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For n=2, a(2)=2+0=2; n=3, a(3)=3+2=5, n=4, a(4)=4+5=9; n=5, a(5)=5+9=14 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 18 2009]
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MAPLE
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seq(sum(k-1, k=3..n), n=2..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 28 2008
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PROGRAM
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(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", "))
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CROSSREFS
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Different from A000096.
Sequence in context: A132336 A000096 A080956 this_sequence A134189 A109470 A112873
Adjacent sequences: A132334 A132335 A132336 this_sequence A132338 A132339 A132340
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KEYWORD
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nonn,new
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Nov 07 2007
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