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

Author

Omar E. Pol, May 23 2010

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A000005, A049820.

Programs

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

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

Extensions

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