A368694 Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).

1, -1, 0, -4, 0, 15, 4, -2, 0, -64, -15, 3, 0, 8, 2, -8, 0, 272, 64, -8, 0, -12, -3, 63, 0, -30, -8, 16, 0, 32, 8, -4, 0, -1144, -272, 20, 0, 32, 8, -512, 0, 45, 12, -126, 0, -252, -63, 15, 0, 128, 30, -24, 0, -64, -16, 32, 0, -120, -32, 8, 0, 16, 4, -2, 0, 4816, 1144, -44, 0, -80, -20, 4160, 0, -120, -32, 1024, 0

Offset: 0

Author

Antti Karttunen, Jan 03 2024

Keywords

• sign
• look

Comments

Scatter plot: "Sailboard congestion".

Links

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

Crossrefs

Cf. A163511, A082903, A366889, A368695 (rgs-transform).

Programs

PARI

A082903(n) = (2^valuation(sigma(n), 2));
memoA366889 = Map();
A366889(n) = if(1==n,1,my(v); if(mapisdefined(memoA366889,n,&v), v, v = -sumdiv(n,d,if(dA082903(n/d)*A366889(d),0)); mapput(memoA366889,n,v); (v)));
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));
A368694(n) = A366889(A163511(n));

Formula

a(n) = A366889(A163511(n)).