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A336477
a(n) = 1 if a regular n-gon is constructible with ruler (or, more precisely, an unmarked straightedge) and compass, 0 otherwise.
9
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, 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, 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
OFFSET
1
COMMENTS
For all n >= 1, a(n) = 1 => A295297(n) = 0.
FORMULA
a(n) = 1 if A005087(n) is equal to A329697(n) [i.e., if A336469(n)=0], and 0 otherwise.
a(n) = A209229(A000010(n)). - Velin Yanev and Antti Karttunen, Mar 02 2021
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
PROG
(PARI)
A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A336477(n) = (omega(n>>valuation(n, 2))==A329697(n));
(PARI)
A209229(n) = (n && !bitand(n, n-1));
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
CROSSREFS
Characteristic function of A003401.
Cf. also A336471, A336923 (analogous sequence for Mersenne primes).
Sequence in context: A187037 A363344 A327866 * A190230 A141679 A276254
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Jul 25 2020
EXTENSIONS
Keyword:mult added by Antti Karttunen, Jan 06 2023
STATUS
approved