A366390 Dirichlet inverse of A366389.

1, -2, -3, 0, -5, 6, -7, 0, 0, 10, -26, 0, -22, 14, 15, 0, -17, 0, -25, 0, 21, 91, -29, 0, 6, 77, 0, 0, -23, -30, -31, 0, 123, 34, -28, 0, -82, 50, 75, 0, -74, -42, -106, -156, 0, 58, -122, 0, -21, -12, 51, -132, -86, 0, 142, 0, 111, 46, -110, 0, -94, 62, 0, 0, 155, -480, -97, 0, 93, 203, -113, 0, -73, 287, -66, 0, 275

Offset: 1

Author

Antti Karttunen, Oct 22 2023

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A010872, A030101, A057889, A073675, A366389, A366392 (rgs-transform).

Cf. also A365711.

Programs

PARI

A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
A073675(n) = if(valuation(n,2)%2,n/2,2*n);
A366389(n) = { my(u=A057889(n)); if(!((u-n)%3),u,A073675(u)); };
memoA366390 = Map();
A366390(n) = if(1==n,1,my(v); if(mapisdefined(memoA366390,n,&v), v, v = -sumdiv(n,d,if(dA366389(n/d)*A366390(d),0)); mapput(memoA366390,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA366389(n/d) * a(d).