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A066839 Sum of positive divisors k of n where k <= sqrt(n). 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums of the table in A161906. - Reinhard Zumkeller, Mar 08 2013

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: Sum_{k>0} k x^(k^2)/(1-x^k). - Michael Somos, Nov 19 2005

EXAMPLE

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.

MAPLE

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);

MATHEMATICA

f[n_] := Plus @@ Select[ Divisors@n, # <= Sqrt@n &]; Array[f, 94] (* Robert G. Wilson v, Mar 04 2010 *)

PROG

(PARI) a(n)=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) ) } \\ Harry J. Smith, Mar 31 2010

(Haskell)

a066839 = sum . a161906_row  -- Reinhard Zumkeller, Mar 08 2013

CROSSREFS

Cf. A070038, A038548, A072499.

Sequence in context: A240833 A110919 A109599 * A176246 A046933 A185091

Adjacent sequences:  A066836 A066837 A066838 * A066840 A066841 A066842

KEYWORD

nonn

AUTHOR

Leroy Quet, Jan 20 2002

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2002

STATUS

approved

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Last modified November 28 14:16 EST 2014. Contains 250361 sequences.