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A070039 Sum of divisors of n that are smaller than sqrt(n). 42
0, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 6, 1, 3, 4, 3, 1, 6, 1, 7, 4, 3, 1, 10, 1, 3, 4, 7, 1, 11, 1, 7, 4, 3, 6, 10, 1, 3, 4, 12, 1, 12, 1, 7, 9, 3, 1, 16, 1, 8, 4, 7, 1, 12, 6, 14, 4, 3, 1, 21, 1, 3, 11, 7, 6, 12, 1, 7, 4, 15, 1, 24, 1, 3, 9, 7, 8, 12, 1, 20, 4, 3, 1, 23, 6, 3, 4, 15, 1, 26, 8, 7, 4, 3, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = sigma(n) - A070038(n).

a(n) = Sum_{n>=1} n*x^(n^2+n)/(1-x^n). - Vladeta Jovovic, Feb 09 2005

EXAMPLE

a(96) = 1+2+3+4+6+8+12 = 36; a(225) = 1+3+5+9 = 18.

MATHEMATICA

di[x_] := Divisors[x] lds[x_] := Ceiling[DivisorSigma[0, x]/2] rd[x_] := Reverse[Divisors[x]] td[x_] := Table[Part[rd[x], w], {w, 1, lds[x]}] sud[x_] := Apply[Plus, td[x]] Table[DivisorSigma[1, w]-sud[w], {w, 1, 128}]

Table[DivisorSum[n, #&, #<Sqrt[n]&], {n, 100}] (* Harvey P. Dale, Oct 26 2015 *)

PROG

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (d^2<n)*d)) /* Michael Somos, Nov 19 2005 */

CROSSREFS

Cf. A038548, A000203, A000005, A070039, A056924.

Sequence in context: A254578 A296120 A050345 * A227991 A319137 A074122

Adjacent sequences:  A070036 A070037 A070038 * A070040 A070041 A070042

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 19 2002

STATUS

approved

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Last modified May 5 19:06 EDT 2021. Contains 343573 sequences. (Running on oeis4.)