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A177235 The number of non-divisors k of n, 1 < k < n, for which floor(n/k) is odd. 4

%I

%S 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,

%T 19,17,21,18,19,21,23,21,24,24,26,24,26,24,28,26,28,32,34,28,30,30,33,

%U 33,35,33,37,35,37,39,41,35,39,39,41,41,42,42,46,44,46,46,50,43,46,46,48

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

%C 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.

%C 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

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv01.jpg">Illustration of the number of divisors of n</a>

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv03.jpg">Illustration of the number of divisors of n (Another version)</a>

%F 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

%p 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:

%p seq(A177235(n),n=1..120) ; # _R. J. Mathar_, May 24 2010

%Y Cf. A000005, A049820.

%K nonn,easy

%O 1,5

%A _Omar E. Pol_, May 23 2010

%E Terms from a(16) onwards from _R. J. Mathar_, May 24 2010

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Last modified February 25 11:54 EST 2020. Contains 332233 sequences. (Running on oeis4.)