A366875 a(n) = A349915(A163511(n)), where A349915 is the Dirichlet inverse of the arithmetic mean between the number and sum of the odd divisors of n.

1, -1, 0, -3, 0, 1, 3, -4, 0, -1, -1, -1, 0, 10, 4, -5, 0, -2, 1, -8, 0, 5, 1, -5, 0, -2, -10, 14, 0, 12, 5, -7, 0, -4, 2, -24, 0, 32, 8, -27, 0, 1, -5, 26, 0, 18, 5, -19, 0, 6, 2, 11, 0, -20, -14, 20, 0, -2, -12, 18, 0, 16, 7, -8, 0, -8, 4, -72, 0, 112, 24, -108, 0, -8, -32, 162, 0, 108, 27, -125, 0, 3, -1, 35, 0

Offset: 0

Author

Antti Karttunen, Oct 27 2023

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A113415, A163511, A349915, A366878 (rgs-transform).

Cf. also A366873.

Programs

PARI

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
memoA349915 = Map();
A349915(n) = if(1==n,1,my(v); if(mapisdefined(memoA349915,n,&v), v, v = -sumdiv(n,d,if(dA113415(n/d)*A349915(d),0)); mapput(memoA349915,n,v); (v)));
A366875(n) = A349915(A163511(n));