cp's OEIS Frontend

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

%I A177235 #13 Jan 06 2017 06:57:48
%S A177235 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 A177235 19,17,21,18,19,21,23,21,24,24,26,24,26,24,28,26,28,32,34,28,30,30,33,
%U A177235 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 A177235 The number of non-divisors k of n, 1 < k < n, for which floor(n/k) is odd.
%C A177235 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 A177235 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 A177235 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv01.jpg">Illustration of the number of divisors of n</a>
%H A177235 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv03.jpg">Illustration of the number of divisors of n (Another version)</a>
%F A177235 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 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 A177235 seq(A177235(n),n=1..120) ; # _R. J. Mathar_, May 24 2010
%Y A177235 Cf. A000005, A049820.
%K A177235 nonn,easy
%O A177235 1,5
%A A177235 _Omar E. Pol_, May 23 2010
%E A177235 Terms from a(16) onwards from _R. J. Mathar_, May 24 2010