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a(n) = A083254(A163511(n)), where A083254(n) = 2*phi(n) - n, the Möbius transform of the deficiency of n.
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%I #14 Oct 24 2023 12:21:15

%S 1,0,0,1,0,3,-2,3,0,9,-6,15,-4,1,-2,5,0,27,-18,75,-12,5,-10,35,-8,3,

%T -14,13,-4,3,-2,9,0,81,-54,375,-36,25,-50,245,-24,15,-70,91,-20,21,

%U -14,99,-16,9,-42,65,-28,-9,-22,43,-8,9,-18,25,-4,7,-2,11,0,243,-162,1875,-108,125,-250,1715,-72,75,-350,637,-100,147,-98,1089

%N a(n) = A083254(A163511(n)), where A083254(n) = 2*phi(n) - n, the Möbius transform of the deficiency of n.

%H Antti Karttunen, <a href="/A324182/b324182.txt">Table of n, a(n) for n = 0..16384</a>

%H Antti Karttunen, <a href="/A324182/a324182.txt">Data supplement: n, a(n) computed for n = 0..65537</a>

%F a(n) = A083254(A163511(n)).

%F For n > 0, a(n) = A324052(A054429(n)).

%o (PARI)

%o A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

%o A083254(n) = (2*eulerphi(n)-n);

%o A324182(n) = A083254(A163511(n));

%Y Cf. A054429, A083254, A163511, A324052, A324183, A324184, A324185 (compare the scatter plot), A366804 (rgs-transform).

%Y Cf. also A324103.

%K sign,look

%O 0,6

%A _Antti Karttunen_, Feb 18 2019