%I A065608
%S A065608 0,1,2,4,4,8,6,11,10,14,10,22,12,20,20,26,16,33,18,36,28,32,22,52,28,
%T A065608 38,36,50,28,64,30,57,44,50,44,82,36,56,52,82,40,88,42,78,72,68,46,114,
%U A065608 54,87,68,92,52,112,68,112,76,86,58,156,60,92,98,120,80,136,66,120,92
%N A065608 Sum of divisors of n minus the number of divisors of n.
%C A065608 Number of permutations p of {1,2,...,n} such that p(k)-k takes exactly 
               two distinct values. Example: a(4)=4 because we have 4123, 3412, 
               2143 and 2341. (Max Alekseyev and Emeric Deutsch) - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Dec 22 2006
%D A065608 M. Alekseev, E. Deutsch, and J. H. Steelman, Problem 11281, Amer. Math. 
               Monthly, 116, No. 5, 2009, p. 465. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 23 2009]
%H A065608 T. D. Noe, <a href="b065608.txt">Table of n, a(n) for n=1..1000</a>
%F A065608 G.f.: sum(k>=1, x^(2k)/(1-x^k)^2) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 21 2003
%F A065608 Starting (1, 2, 4, 4, 8, 6,...), = row sums of triangle A077478. - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Nov 12 2007
%F A065608 a(n) = sigma(n)-d(n) = A000203(n)-A000005(n). [From Omar E. Pol (info(AT)polprimos.com), 
               Dec 12 2008]
%p A065608 with(numtheory): seq(sigma(n)-tau(n),n=1..70); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Dec 22 2006
%o A065608 (PARI) { for (n = 1, 1000, a=sigma(n) - numdiv(n); write("b065608.txt", 
               n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Oct 23 2009]
%Y A065608 Cf. A000203, A000005.
%Y A065608 Cf. A134857.
%Y A065608 Sequence in context: A107748 A005884 A079890 this_sequence A077764 A110794 
               A117295
%Y A065608 Adjacent sequences: A065605 A065606 A065607 this_sequence A065609 A065610 
               A065611
%K A065608 nonn
%O A065608 1,3
%A A065608 Jason Earls (zevi_35711(AT)yahoo.com), Nov 06 2001