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

1,25

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

Formula

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

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

Prog

(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));

Crossrefs

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

Cf. also A347374.

Sequence in context: A133703 A073265 A338326 * A025438 A220400 A285108

Adjacent sequences: A347246 A347247 A347248 * A347250 A347251 A347252

Keyword

sign

Author

Antti Karttunen, Aug 28 2021

Status

approved