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A305804 Möbius-transform of A078898.

%I A305804 #5 Jun 13 2018 23:10:45
%S A305804 1,0,0,1,0,2,0,2,1,4,0,2,0,6,2,4,0,5,0,4,3,10,0,4,1,12,3,6,0,6,0,8,5,
%T A305804 16,2,6,0,18,6,8,0,9,0,10,4,22,0,8,1,19,8,12,0,15,3,12,9,28,0,8,0,30,
%U A305804 6,16,4,15,0,16,11,22,0,12,0,36,9,18,2,18,0,16,9,40,0,12,5,42,14,20,0,20,3,22,15,46,6,16,0,41,10,20,0,24,0,24,10
%N A305804 Möbius-transform of A078898.
%H A305804 Antti Karttunen, <a href="/A305804/b305804.txt">Table of n, a(n) for n = 1..65537</a>
%F A305804 a(n) = Sum_{d|n} A008683(n/d)*A078898(d).
%o A305804 (PARI)
%o A305804 up_to = 65537;
%o A305804 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 A305804 A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
%o A305804 v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
%o A305804 A078898(n) = v078898[n];
%o A305804 A305804(n) = sumdiv(n,d,moebius(n/d)*A078898(d));
%Y A305804 Cf. A008683, A078898, A305798, A305803.
%K A305804 nonn
%O A305804 1,6
%A A305804 _Antti Karttunen_, Jun 13 2018