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A305797 Dirichlet convolution of A078898 with A078899.

%I A305797 #5 Jun 13 2018 09:12:12
%S A305797 1,2,2,5,2,7,2,11,6,9,2,19,2,11,8,23,2,24,2,25,9,15,2,45,8,17,17,31,2,
%T A305797 39,2,47,11,21,10,66,2,23,12,62,2,48,2,43,27,27,2,100,10,48,14,49,2,
%U A305797 76,11,79,15,33,2,113,2,35,32,95,12,66,2,61,17,69,2,161,2,41,37,67,12,75,2,142,44,45,2,142,13,47,20,111,2,143,13,79,21,51,14
%N A305797 Dirichlet convolution of A078898 with A078899.
%H A305797 Antti Karttunen, <a href="/A305797/b305797.txt">Table of n, a(n) for n = 1..65537</a>
%F A305797 a(n) = Sum_{d|n} A078898(d)*A078899(n/d).
%o A305797 (PARI)
%o A305797 up_to = 65537;
%o A305797 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 A305797 A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
%o A305797 A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
%o A305797 v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
%o A305797 A078898(n) = v078898[n];
%o A305797 v078899 = ordinal_transform(vector(up_to,n,A006530(n)));
%o A305797 A078899(n) = v078899[n];
%o A305797 A305797(n) = sumdiv(n,d,A078898(d)*A078899(n/d));
%Y A305797 Cf. A078898, A078899, A305798, A305799.
%K A305797 nonn
%O A305797 1,2
%A A305797 _Antti Karttunen_, Jun 13 2018