Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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