cp's OEIS Frontend

A334862 a(n) = A334097(n) - A064415(n).

%I A334862 #8 May 14 2020 21:22:34
%S A334862 0,0,1,0,1,1,1,0,2,1,1,1,1,1,2,0,1,2,2,1,2,1,1,1,2,1,3,1,2,2,1,0,2,1,
%T A334862 2,2,2,2,2,1,1,2,2,1,3,1,1,1,2,2,2,1,2,3,2,1,3,2,2,2,1,1,3,0,2,2,2,1,
%U A334862 2,2,2,2,2,2,3,2,2,2,2,1,4,1,1,2,2,2,3,1,2,3,2,1,2,1,3,1,1,2,3,2,2,2,1,1,3
%N A334862 a(n) = A334097(n) - A064415(n).
%C A334862 Completely additive because A064415 and A334097 are.
%H A334862 Antti Karttunen, <a href="/A334862/b334862.txt">Table of n, a(n) for n = 1..65537</a>
%F A334862 a(2) = 0, a(p) = A334097(p+1)-A064415(p-1) for odd primes p, a(m*n) = a(m)+a(n), if m,n > 1.
%F A334862 a(n) = A334097(n) - A064415(n).
%F A334862 a(3^k) = k for all k>= 0.
%o A334862 (PARI)
%o A334862 A064415(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],f[k,2],f[k,2]*A064415(f[k,1]-1))); };
%o A334862 A334097(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],f[k,2],f[k,2]*A334097(f[k,1]+1))); };
%o A334862 A334862(n) = (A334097(n)-A064415(n));
%o A334862 \\ Or alternatively as:
%o A334862 A334862(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(A334097(f[k,1]+1)-A064415(f[k,1]-1)))); };
%Y A334862 Cf. A000079 (positions of zeros), A000244, A064415, A334097, A334861.
%K A334862 nonn
%O A334862 1,9
%A A334862 _Antti Karttunen_, May 14 2020