%I #23 Jan 08 2023 14:25:53

%S 1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,1,

%T 0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,

%U 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0

%N a(n) = 1 if a regular n-gon is constructible with ruler (or, more precisely, an unmarked straightedge) and compass, 0 otherwise.

%C For all n >= 1, a(n) = 1 => A295297(n) = 0.

%H Antti Karttunen, <a href="/A336477/b336477.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = 1 if A005087(n) is equal to A329697(n) [i.e., if A336469(n)=0], and 0 otherwise.

%F a(n) = A209229(A000010(n)). - _Velin Yanev_ and _Antti Karttunen_, Mar 02 2021

%F Multiplicative with a(2^e) = 1, and for odd primes p, a(p^e) = A209229(p-1) if e = 1, and 0 if e > 1. - _Antti Karttunen_, Jan 06 2023

%o (PARI)

%o A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));

%o A336477(n) = (omega(n>>valuation(n,2))==A329697(n));

%o (PARI)

%o A209229(n) = (n && !bitand(n,n-1));

%o A336477(n) = { my(f=factor(n)); prod(k=1,#f~,(2==f[k,1] || A209229(f[k,1]-1)*(1==f[k,2]))); }; \\ _Antti Karttunen_, Jan 06 2023

%Y Characteristic function of A003401.

%Y Cf. A000010, A000265, A001221, A005087, A209229, A295297, A329697, A336469, A359578 (Dirichlet inverse).

%Y Cf. also A336471, A336923 (analogous sequence for Mersenne primes).

%K nonn,mult

%O 1

%A _Antti Karttunen_, Jul 25 2020

%E Keyword:mult added by _Antti Karttunen_, Jan 06 2023