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A066839
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Sum of positive divisors k of n where k <= sqrt(n).
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10
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1, 1, 1, 3, 1, 3, 1, 3, 4, 3, 1, 6, 1, 3, 4, 7, 1, 6, 1, 7, 4, 3, 1, 10, 6, 3, 4, 7, 1, 11, 1, 7, 4, 3, 6, 16, 1, 3, 4, 12, 1, 12, 1, 7, 9, 3, 1, 16, 8, 8, 4, 7, 1, 12, 6, 14, 4, 3, 1, 21, 1, 3, 11, 15, 6, 12, 1, 7, 4, 15, 1, 24, 1, 3, 9, 7, 8, 12, 1, 20, 13, 3, 1, 23, 6, 3, 4, 15, 1, 26, 8, 7, 4, 3
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OFFSET
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1,4
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COMMENTS
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Row sums of the table in A161906. - Reinhard Zumkeller, Mar 08 2013
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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G.f.: Sum_{k>0} k x^(k^2)/(1-x^k) . - Michael Somos Nov 19 2005
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EXAMPLE
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a(9) = 4 = 1 + 3 because 1 and 3 are the positive divisors of 9 that are <= sqrt(9).
a(20) = 7: the divisors of 20 are 1,2,4,5,10 and 20. a(20) = 1 + 2 + 4= 7.
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MAPLE
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with(numtheory):for n from 1 to 200 do c[n] := 0:d := divisors(n):for i from 1 to nops(d) do if d[i]<=n^.5+10^(-10) then c[n] := c[n]+d[i]:fi:od:od:seq(c[i], i=1..200);
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MATHEMATICA
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f[n_] := Plus @@ Select[ Divisors@n, # <= Sqrt@n &]; Array[f, 94] [From Robert G. Wilson v, Mar 04 2010]
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PROG
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (d^2<=n)*d)) /* Michael Somos Nov 19 2005 */
(PARI) { for (n=1, 1000, d=divisors(n); s=sum(k=1, ceil(length(d)/2), d[k]); write("b066839.txt", n, " ", s) ) } [From Harry J. Smith, Mar 31 2010]
(Haskell)
a066839 = sum . a161906_row -- Reinhard Zumkeller, Mar 08 2013
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CROSSREFS
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Cf. A070038.
Cf. A038548, A072499.
Sequence in context: A001319 A110919 A109599 * A046933 A185091 A023511
Adjacent sequences: A066836 A066837 A066838 * A066840 A066841 A066842
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Jan 20 2002
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2002
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STATUS
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approved
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