A347249 - OEIS

%I #9 Jan 30 2022 09:50:56

%S 0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,-1,-1,0,0,1,0,0,0,2,0,0,0,1,1,0,0,1,

%T -1,1,-1,0,0,1,0,1,1,0,0,1,0,0,0,-2,2,0,0,0,0,0,0,1,1,1,1,0,0,0,0,2,1,

%U -1,-1,1,1,-1,-1,0,0,3,0,1,1,0,0,-1,1,1,1,1,0,2,0,1,1,1,0,1,0,2,0,-2,-2,1,2

%N a(n) = A331410(n) - A336361(n).

%C Terms 0 .. 9 occur for the first time at n = 1, 15, 25, 75, 275, 725, 2175, 3725, 9025, 27075.

%H Antti Karttunen, <a href="/A347249/b347249.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A331410(n) - A336361(n).

%F For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

%o (PARI)

%o A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };

%o A336361(n) = if(!bitand(n,n-1),0,1+A336361(sigma(n>>valuation(n,2))));

%o A347249(n) = (A331410(n)-A336361(n));

%Y Cf. A000265, A331410, A336361, A347250 (positions of negative terms).

%Y Cf. also A347374.

%K sign

%O 1,25

%A _Antti Karttunen_, Aug 28 2021