cp's OEIS Frontend

A305803 Dirichlet inverse of A078898.

%I A305803 #5 Jun 13 2018 23:10:39
%S A305803 1,-1,-1,-1,-1,-1,-1,-1,-1,-3,-1,1,-1,-5,-1,-1,-1,-2,-1,1,-2,-9,-1,3,
%T A305803 -1,-11,-2,1,-1,1,-1,-1,-4,-15,-1,5,-1,-17,-5,5,-1,1,-1,1,-1,-21,-1,5,
%U A305803 -1,-14,-7,1,-1,-4,-2,7,-8,-27,-1,17,-1,-29,-2,-1,-3,1,-1,1,-10,-11,-1,8,-1,-35,-6,1,-1,1,-1,9,-5,-39,-1,26,-4,-41,-13,11,-1,6,-2,1
%N A305803 Dirichlet inverse of A078898.
%H A305803 Antti Karttunen, <a href="/A305803/b305803.txt">Table of n, a(n) for n = 1..65537</a>
%F A305803 a(1) = 1; for n > 1, a(n) = -Sum_{d|n, d<n} A078898(n/d)*a(d).
%o A305803 (PARI)
%o A305803 up_to = 65537;
%o A305803 ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o A305803 A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
%o A305803 v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
%o A305803 A078898(n) = v078898[n];
%o A305803 A305803(n) = if(1==n,1,-sumdiv(n,d,if(d<n,A078898(n/d)*A305803(d),0)));
%Y A305803 Cf. A078898, A305798, A305804.
%K A305803 sign
%O A305803 1,10
%A A305803 _Antti Karttunen_, Jun 13 2018