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%I A344884 #9 Jun 30 2021 10:33:02
%S A344884 1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,1,1,1,1,1,1,0,1,1,0,1,
%T A344884 0,1,1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,
%U A344884 0,0,1,0,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0
%N A344884 a(n) = 1 if A011772(n) divides A344875(n), otherwise 0; characteristic function of A344974.
%H A344884 Antti Karttunen, <a href="/A344884/b344884.txt">Table of n, a(n) for n = 1..65537</a>
%H A344884 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A344884 a(n) >= A344885(n) >= A010055(n).
%o A344884 (PARI)
%o A344884 A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
%o A344884 A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
%o A344884 A344884(n) = !(A344875(n)%A011772(n));
%Y A344884 Characteristic function of A344974.
%Y A344884 Cf. A010055, A011772, A344875, A344880, A344885.
%K A344884 nonn
%O A344884 1
%A A344884 _Antti Karttunen_, Jun 05 2021

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