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%I #17 Jul 04 2024 09:21:33
%S 1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,0,
%T 0,0,1,1,0,1,0,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,1,0,1,1,0,0,1,
%U 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0
%N a(n) = 1 if n is a number of the form x^2 + xy + y^2, otherwise 0.
%C a(n) = 1 iff in the prime factorization of n, all primes == 2 (mod 3) occur to even powers.
%H Antti Karttunen, <a href="/A353816/b353816.txt">Table of n, a(n) for n = 0..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = [A088534(n) > 0], where [ ] is the Iverson bracket.
%F a(n) >= A353815(n).
%F Multiplicative with a(p^e) = 0 if p == 2 (mod 3) and e is odd, and a(p^e) = 1 in all other cases. - _Antti Karttunen_, Jul 04 2024
%o (PARI) A353816(n) = if(!n, 1, my(f=factor(n), flag=1); for(i=1, #f~, if(Mod(f[i, 1], 3)==2 && Mod(f[i, 2], 2)==1, flag=0)); (flag)); \\ After function isA003136 in A003136.
%o (PARI) A353816(n) = if(!n, 1, my(f=factor(n)); prod(i=1, #f~, (2!=(f[i, 1]%3) || (1+f[i, 2])%2))); \\ _Antti Karttunen_, Jul 04 2024
%Y Characteristic function of A003136.
%Y Cf. A088534, A353815.
%K nonn,mult,changed
%O 0
%A _Antti Karttunen_, May 15 2022
%E Keyword:mult added by _Antti Karttunen_, Jul 04 2024
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