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Dirichlet convolution of Liouville's lambda with A342001 applied to Doudna sequence: a(n) = A347395(A005940(1+n)).
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%I #8 Oct 26 2023 13:22:28

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

%H Antti Karttunen, <a href="/A366803/b366803.txt">Table of n, a(n) for n = 0..16384</a>

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A342001(n) = (A003415(n) / A003557(n));

%o A008836(n) = ((-1)^bigomega(n));

%o A347395(n) = sumdiv(n,d,A008836(n/d)*A342001(d));

%o A366803(n) = A347395(A005940(1+n));

%Y Cf. A003415, A005940, A008836, A342001, A347395, A366805 (rgs-transform).

%Y Cf. also A347396, A366795, A366801.

%K nonn

%O 0,6

%A _Antti Karttunen_, Oct 26 2023