A334862 - OEIS

%I #8 May 14 2020 21:22:34

%S 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 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 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 a(n) = A334097(n) - A064415(n).

%C Completely additive because A064415 and A334097 are.

%H Antti Karttunen, <a href="/A334862/b334862.txt">Table of n, a(n) for n = 1..65537</a>

%F 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 a(n) = A334097(n) - A064415(n).

%F a(3^k) = k for all k>= 0.

%o (PARI)

%o 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 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(n) = (A334097(n)-A064415(n));

%o \\ Or alternatively as:

%o 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 Cf. A000079 (positions of zeros), A000244, A064415, A334097, A334861.

%K nonn

%O 1,9

%A _Antti Karttunen_, May 14 2020