A335875 a(n) = min(A329697(n), A331410(n)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jun 29 2020

Keywords

• nonn

Examples

			A329697(67) = A331410(67) = 4, thus a(67) = min(4,4) = 4.
A329697(15749) = 9 and A331410(15749) = 10, thus a(15749) = 9.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

Programs

PARI

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

Formula

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

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