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A366803 Dirichlet convolution of Liouville's lambda with A342001 applied to Doudna sequence: a(n) = A347395(A005940(1+n)).

%I A366803 #8 Oct 26 2023 13:22:28
%S A366803 0,1,1,1,1,3,1,2,1,5,6,3,1,2,2,2,1,7,8,5,10,14,5,5,1,2,3,2,2,4,2,3,1,
%T A366803 11,12,7,14,20,7,9,16,34,44,14,7,9,10,5,1,2,3,2,5,5,2,3,2,6,8,4,2,3,3,
%U A366803 3,1,13,14,11,16,32,11,13,18,54,68,20,11,13,14,9,22,76,92,34,124,92,34,22,11,13,20,9,16
%N A366803 Dirichlet convolution of Liouville's lambda with A342001 applied to Doudna sequence: a(n) = A347395(A005940(1+n)).
%H A366803 Antti Karttunen, <a href="/A366803/b366803.txt">Table of n, a(n) for n = 0..16384</a>
%o A366803 (PARI)
%o A366803 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A366803 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A366803 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A366803 A342001(n) = (A003415(n) / A003557(n));
%o A366803 A008836(n) = ((-1)^bigomega(n));
%o A366803 A347395(n) = sumdiv(n,d,A008836(n/d)*A342001(d));
%o A366803 A366803(n) = A347395(A005940(1+n));
%Y A366803 Cf. A003415, A005940, A008836, A342001, A347395, A366805 (rgs-transform).
%Y A366803 Cf. also A347396, A366795, A366801.
%K A366803 nonn
%O A366803 0,6
%A A366803 _Antti Karttunen_, Oct 26 2023