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A354185 Möbius transform of A348717.

%I A354185 #10 May 19 2022 16:42:57
%S A354185 1,1,1,2,1,3,1,4,2,7,1,4,1,11,3,8,1,10,1,8,7,19,1,8,2,23,4,12,1,13,1,
%T A354185 16,11,31,3,12,1,35,19,16,1,17,1,20,4,43,1,16,2,38,23,24,1,32,7,24,31,
%U A354185 55,1,16,1,59,8,32,11,29,1,32,35,45,1,24,1,71,10,36,3,29,1,32,8,79,1,24,19,83,43,40,1,44,7
%N A354185 Möbius transform of A348717.
%C A354185 Question: Are all terms positive?
%H A354185 Antti Karttunen, <a href="/A354185/b354185.txt">Table of n, a(n) for n = 1..10000</a>
%H A354185 Antti Karttunen, <a href="/A354185/a354185.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A354185 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A354185 a(n) = Sum_{d|n} A008683(n/d) * A348717(d).
%o A354185 (PARI)
%o A354185 A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
%o A354185 A354185(n) = sumdiv(n,d,moebius(n/d)*A348717(d));
%Y A354185 Cf. A008683, A348717.
%Y A354185 Cf. also A322994.
%K A354185 nonn
%O A354185 1,4
%A A354185 _Antti Karttunen_, May 19 2022