A069289 Sum of odd divisors of n <= sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 6, 1, 4, 1, 1, 9, 1, 1, 4, 1, 6, 4, 1, 1, 4, 6, 1, 4, 1, 1, 9, 1, 1, 4, 8, 6, 4, 1, 1, 4, 6, 8, 4, 1, 1, 9, 1, 1, 11, 1, 6, 4, 1, 1, 4, 13, 1, 4, 1, 1, 9, 1, 8, 4, 1, 6, 13, 1, 1, 11, 6, 1, 4, 1

Offset: 1

Author

Reinhard Zumkeller, Mar 14 2002

Keywords

• nonn

Comments

a(n) = Sum{d : d = A182469(n,k), d <= A000196(n), k=1..A001227(n)}. - Reinhard Zumkeller, Apr 05 2015

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000593, A000203, A069288.

Cf. A000196, A182469, A001227.

Programs

Haskell

a069289 n = sum $ takeWhile (<= a000196 n) $ a182469_row n
-- Reinhard Zumkeller, Apr 05 2015

Mathematica

Table[Total[Select[Divisors[n],OddQ[#]&&#<=Sqrt[n]&]],{n,120}] (* Harvey P. Dale, Jul 16 2017 *)

PARI

a(n) = my(ir = sqrtint(n)); sumdiv(n, d, (d % 2) * (d <= ir) * d); \\ Michel Marcus, Jan 14 2014

Formula

G.f.: Sum_{k>=1} (2*k - 1) * x^((2*k - 1)^2) / (1 - x^(2*k - 1)). - Ilya Gutkovskiy, Apr 04 2020