A177235 - OEIS

A177235

The number of non-divisors k of n, 1 < k < n, for which floor(n/k) is odd.

0, 0, 1, 1, 2, 2, 4, 3, 4, 5, 7, 5, 7, 7, 9, 9, 10, 9, 12, 10, 12, 14, 16, 12, 14, 15, 17, 17, 19, 17, 21, 18, 19, 21, 23, 21, 24, 24, 26, 24, 26, 24, 28, 26, 28, 32, 34, 28, 30, 30, 33, 33, 35, 33, 37, 35, 37, 39, 41, 35, 39, 39, 41, 41, 42, 42, 46, 44, 46, 46, 50, 43, 46, 46, 48

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

See the illustration in the second link: a(n) is the number of arcs that are intercepted by a vertical line intersecting the abscissa at n.

Sum of the differences of the number of divisors of the largest parts and the number of divisors of the smallest parts of the partitions of n into two parts. - Wesley Ivan Hurt, Jan 05 2017

LINKS

Table of n, a(n) for n=1..75.

Omar E. Pol, Illustration of the number of divisors of n

Omar E. Pol, Illustration of the number of divisors of n (Another version)

FORMULA

a(n) = Sum_{i=1..floor(n/2)} d(n-i) - d(i) where d(n) is the number of divisors of n. - Wesley Ivan Hurt, Jan 05 2017

MAPLE

A177235 := proc(n) local a; a :=0 ; for k from 1 to n-1 do if n mod k <> 0 and type(floor(n/k), 'odd') then a := a+1 ; end if; end do: a ; end proc:

seq(A177235(n), n=1..120) ; # R. J. Mathar, May 24 2010

CROSSREFS

Cf. A000005, A049820.

Sequence in context: A015134 A171580 A246796 * A079707 A233511 A205793