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A347230 Möbius transform of A344695, gcd(sigma(n), psi(n)).

%I A347230 #17 Aug 26 2021 16:07:03
%S A347230 1,2,3,-2,5,6,7,2,-3,10,11,-6,13,14,15,-2,17,-6,19,-10,21,22,23,6,-5,
%T A347230 26,3,-14,29,30,31,2,33,34,35,6,37,38,39,10,41,42,43,-22,-15,46,47,-6,
%U A347230 -7,-10,51,-26,53,6,55,14,57,58,59,-30,61,62,-21,-2,65,66,67,-34,69,70,71,-6,73,74,-15,-38,77,78,79
%N A347230 Möbius transform of A344695, gcd(sigma(n), psi(n)).
%C A347230 Not multiplicative because A344695 isn't either. For example, a(4) = -2, a(27) = 3, but a(108) = -2 != -6.
%C A347230 The absolute values are not equal to A007947. The first n where abs(a(n)) != A007947(n) is at n=108, with a(108) = -2, while A007947(108) = 6.
%C A347230 The first n such that a(n) does not divide n are: 196, 216, 392, 432, 441, 588, etc.
%C A347230 The zeros occur at n = 288, 576, 1440, 2016, 2880, 3168, 3744, 4032, etc.
%H A347230 Antti Karttunen, <a href="/A347230/b347230.txt">Table of n, a(n) for n = 1..16384</a>
%F A347230 a(n) = Sum_{d|n} A008683(n/d) * A344695(d).
%F A347230 a(n) = A344695(n) - A347231(n).
%o A347230 (PARI)
%o A347230 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A347230 A344695(n) = gcd(sigma(n), A001615(n));
%o A347230 A347230(n) = sumdiv(n,d,moebius(n/d)*A344695(d));
%Y A347230 Cf. A000203, A001615, A008683, A344695, A347228, A347231.
%Y A347230 Cf. also A007947, A063659.
%K A347230 sign
%O A347230 1,2
%A A347230 _Antti Karttunen_, Aug 25 2021