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

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

Adjacent sequences: A177232 A177233 A177234 * A177236 A177237 A177238

Keyword

nonn,easy

Author

Omar E. Pol, May 23 2010

Extensions

Terms from a(16) onwards from R. J. Mathar, May 24 2010

Status

approved