%I A101172
%S A101172 1,2,3,5,8,15,26,51,97,191,373,745,1472,2943,5859,11708,23365,46729,
%T A101172 93349,186697,373200,746372,1492370,2984739,5968687,11937366,23873259,
%U A101172 47746421,95489896,190979791,381953529,763907057,1527790748,1527802406
%N A101172 Sequence whose Mobius transform leads to the first differences of the 
               terms.
%C A101172 In the example, the last value in the Mobius transform of [1,2,3,5,8] 
               is 7 and so the next term in our sequence is 8+7=15. Then, the Mobius 
               transform of [1,2,3,5,8,15] is [1,1,2,3,7,11], which means that the 
               next term of our sequence is 15+11=26, etc.
%e A101172 For example, the Mobius transform of the segment [1,2,3,5,8] begins [1,
               1,2,3], which are the first differences of these terms.
%p A101172 with(numtheory): F:={1}: f:=n->F[n]: g:=n->sum(mobius(divisors(n)[j])*f(n/
               divisors(n)[j]),j=1..tau(n)): for n from 1 to 35 do F:=F union {F[nops(F)]+g(n)} 
               od: G:=sort(convert(F,list)); (Deutsch)
%Y A101172 Sequence in context: A054539 A026702 A000047 this_sequence A006544 A110536 
               A049861
%Y A101172 Adjacent sequences: A101169 A101170 A101171 this_sequence A101173 A101174 
               A101175
%K A101172 easy,nonn
%O A101172 1,2
%A A101172 Mark Hudson (mrmarkhudson(AT)hotmail.com), Dec 03 2004
%E A101172 Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Feb 15 2005