A347249 a(n) = A331410(n) - A336361(n).

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

Offset: 1

Author

Antti Karttunen, Aug 28 2021

Keywords

• sign

Comments

Terms 0 .. 9 occur for the first time at n = 1, 15, 25, 75, 275, 725, 2175, 3725, 9025, 27075.

Links

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

Crossrefs

Cf. A000265, A331410, A336361, A347250 (positions of negative terms).

Cf. also A347374.

Programs

PARI

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)))); };
A336361(n) = if(!bitand(n,n-1),0,1+A336361(sigma(n>>valuation(n,2))));
A347249(n) = (A331410(n)-A336361(n));

Formula

a(n) = A331410(n) - A336361(n).

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).