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a(n) = Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * 2^(d-1).
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%I #7 Apr 15 2021 21:41:08

%S 1,1,3,7,15,27,63,127,255,495,1023,2037,4095,8127,16365,32767,65535,

%T 130815,262143,524265,1048509,2096127,4194303,8388477,16777215,

%U 33550335,67108863,134217657,268435455,536854005,1073741823,2147483647,4294966269,8589869055,17179869105

%N a(n) = Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * 2^(d-1).

%F a(n) = 2^(n-1) - Sum_{d|n, gcd(d, n/d) = 1, d < n} a(d).

%t a[n_] := Sum[If[GCD[d, n/d] == 1, (-1)^PrimeNu[n/d] 2^(d - 1), 0], {d, Divisors[n]}]; Table[a[n], {n, 35}]

%o (PARI) a(n) = sumdiv(n, d, if (gcd(d, n/d)==1, (-1)^omega(n/d) * 2^(d-1))); \\ _Michel Marcus_, Apr 15 2021

%Y Cf. A000740, A001221, A011782, A076479.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Apr 15 2021