A365713 Dirichlet inverse of reversing binary value of n (A065620).

1, -2, 1, 0, 3, -2, -3, 0, 8, -6, -7, 0, -5, 6, 11, 0, 15, -16, -15, 0, -19, 14, 13, 0, 0, 10, 24, 0, 11, -22, -11, 0, 17, -30, -49, 0, -29, 30, 19, 0, -25, 38, 25, 0, 88, -26, -27, 0, -8, 0, 47, 0, 19, -48, -61, 0, -7, -22, -23, 0, -21, 22, -56, 0, 33, -34, -63, 0, -35, 98, 61, 0, -57, 58, 96, 0, 101, -38, -59, 0

Offset: 1

Author

Antti Karttunen, Sep 19 2023

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A065620, A365714.

Cf. also A355819, A365711.

Programs

PARI

A065620(n, c=1) = sum(i=0, logint(n+!n, 2), if(bittest(n, i), (-1)^c++<A065620 by M. F. Hasler
memoA365713 = Map();
A365713(n) = if(1==n,1,my(v); if(mapisdefined(memoA365713,n,&v), v, v = -sumdiv(n,d,if(dA065620(n/d)*A365713(d),0)); mapput(memoA365713,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA065620(n/d) * a(d).