A335875 - OEIS

%I #11 Jun 30 2020 00:16:10

%S 0,0,1,0,1,1,1,0,2,1,2,1,2,1,2,0,1,2,3,1,2,2,2,1,2,2,3,1,3,2,1,0,3,1,

%T 3,2,3,3,3,1,2,2,3,2,3,2,2,1,2,2,2,2,3,3,3,1,4,3,4,2,2,1,3,0,3,3,4,1,

%U 3,3,3,2,3,3,3,3,3,3,3,1,4,2,3,2,2,3,4,2,3,3,3,2,2,2,4,1,2,2,4,2,3,2,3,2,4

%N a(n) = min(A329697(n), A331410(n)).

%H Antti Karttunen, <a href="/A335875/b335875.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = min(A329697(n), A331410(n)).

%F For all n >= 1, A335904(n) >= A335884(n) >= A335881(n) >= a(n) >= A335885(n).

%e A329697(67) = A331410(67) = 4, thus a(67) = min(4,4) = 4.

%e A329697(15749) = 9 and A331410(15749) = 10, thus a(15749) = 9.

%o (PARI)

%o A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };

%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 A335875(n) = min(A329697(n),A331410(n));

%Y Cf. A329697, A331410, A334861, A335877, A335881, A335884, A335885, A335904.

%K nonn

%O 1,9

%A _Antti Karttunen_, Jun 29 2020