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Search: id:A060831
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| A060831 |
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Number of sums less than or equal to n of sequences of consecutive positive integers (including sequences of length 1). |
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+0
4
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| 0, 1, 2, 4, 5, 7, 9, 11, 12, 15, 17, 19, 21, 23, 25, 29, 30, 32, 35, 37, 39, 43, 45, 47, 49, 52, 54, 58, 60, 62, 66, 68, 69, 73, 75, 79, 82, 84, 86, 90, 92, 94, 98, 100, 102, 108, 110, 112, 114, 117, 120, 124, 126, 128, 132, 136, 138, 142, 144, 146, 150, 152, 154, 160
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of odd divisors present in [1,..,n]. E.g. for a(7), we consider the odd divisors of 1,2,3,4,5,6,7, which gives 1,1,2,1,2,2,2=11. - Jon Perry (perry(AT)globalnet.co.uk), Mar 22 2004
Starting with 1 = row sums of triangle A168508 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 27 2009]
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
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a(n) = n+[n/3]+[n/5]+[n/7]+[n/9]+... = a(n-1)+A001227(n) = A006218(n)-A006218([n/2]).
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EXAMPLE
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a(7) = 11 since 1, 2, 3, 4, 5, 6, 7, 1+2, 2+3, 3+4, 1+2+3 are all 7 or less.
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MATHEMATICA
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f[n_] := Sum[ -(-1^k)Floor[n/(2k - 1)], {k, n}]; Table[ f[n], {n, 0, 65}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jun 16 2006)
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PROGRAM
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(PARI) a(n)=local(c); c=0; for(i=1, n, c+=sumdiv(i, X, X%2)); c for(i=1, 100, print1(", "a(i)))
(PARI) { for (n=0, 1000, s=n; d=3; while (n>=d, s+=n\d; d+=2); write("b060831.txt", n, " ", s); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 12 2009]
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CROSSREFS
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Sequence in context: A093848 A049039 A005152 this_sequence A073727 A075692 A112235
Adjacent sequences: A060828 A060829 A060830 this_sequence A060832 A060833 A060834
Cf. A168508 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 27 2009]
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KEYWORD
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nonn,new
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 01 2001
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