%I A109506
%S A109506 1,3,4,3,6,12,8,3,13,18,12,12,14,24,24,3,18,39,20,18,32,36,24,12,31,42,
%T A109506 40,24,30,72,32,3,48,54,48,39,38,60,56,18,42,96,44,36,78,72,48,12,57,93,
%U A109506 72,42,54,120,72,24,80,90,60,72,62,96,104,3,84,144,68,54,96,144,72
%V A109506 1,-3,4,-3,6,-12,8,-3,13,-18,12,-12,14,-24,24,-3,18,-39,20,-18,32,-36,
               24,-12,31,-42,40,
%W A109506 -24,30,-72,32,-3,48,-54,48,-39,38,-60,56,-18,42,-96,44,-36,78,-72,48,
               -12,57,-93,72,
%X A109506 -42,54,-120,72,-24,80,-90,60,-72,62,-96,104,-3,84,-144,68,-54,96,-144,
               72
%N A109506 Expansion of (1-eta(q)^8/et(q^2)^4)/8 in powers of q.
%D A109506 G. Chrystal, Algebra: An elementary text-book for the higher classes 
               of secondary schools and for colleges, 6th ed, Chelsea Publishing 
               Co., New York 1959 Part II, p. 346 Exercise XXI(18). MR0121327 (22 
               #12066)
%F A109506 a(n) = Sum_{d divides n} (-1)^(n/d+d)*d.
%F A109506 Multiplicative with a(2^e) = -3, if e>0. a(p^e) = (p^(e+1)-1)/(p-1) if 
               p>2.
%F A109506 G.f.: Sum_{k>0} k(x^k/(1-x^k) -6x^(2k)/(1-x^(2k)) +8x^(4k)/(1-x^(4k))).
%F A109506 G.f.: Sum_{k>0} -(-x)^k/(1+x^k)^2 = Sum_{k>0} -k*(-x)^k/(1+x^k).
%o A109506 (PARI) a(n)=if(n<1,0,-(-1)^n*sumdiv(n,d,if(d%4,d)))
%o A109506 (PARI) {a(n)=local(A); if(n<1, 0, A=x*O(x^n); -1/8*polcoeff( eta(x+A)^8/
               eta(x^2+A)^4, n))}
%Y A109506 a(n)=-(-1)^n*A046897(n). a(n)=-A096727(n)/8, if n>0.
%Y A109506 Sequence in context: A048250 A073181 A046897 this_sequence A000113 A069915 
               A033634
%Y A109506 Adjacent sequences: A109503 A109504 A109505 this_sequence A109507 A109508 
               A109509
%K A109506 sign,mult
%O A109506 1,2
%A A109506 Michael Somos, Jun 30 2005