A336396 a(n) = A329697(n) - A087436(n).

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 2, 0, 1, 1, 2, 0, 0, 1, 0, 1, 2, 0, 2, 0, 1, 0, 1, 0, 2, 2, 1, 0, 1, 1, 3, 1, 0, 2, 3, 0, 2, 0, 0, 1, 2, 0, 1, 1, 2, 2, 3, 0, 2, 2, 1, 0, 1, 1, 3, 0, 2, 1, 3, 0, 2, 2, 0, 2, 2, 1, 3, 0, 0, 1, 2, 1, 0, 3, 2, 1, 2, 0, 2, 2, 2, 3, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 1

Offset: 1

Author

Antti Karttunen, Jul 24 2020

Keywords

• nonn

Comments

Totally additive because both A087436 and A329697 are.

Links

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

Crossrefs

Cf. A000265, A046660, A087436, A329697, A336118, A336466, A336469.

Programs

PARI

A087436(n) = (bigomega(n>>valuation(n,2)));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A336396(n) = (A329697(n) - A087436(n));

Formula

a(n) = A329697(n) - A087436(n).

a(n) = A329697(A336466(n)).

a(n) = A336469(n) - A046660(A000265(n)).

For all n >= 1, a(n) <= A336118(n).