A378757 Dirichlet convolution of sigma and the Dirichlet inverse of A005187 (A346237).

1, 0, 0, 0, -2, 2, -3, 0, -3, 6, -7, 0, -9, 8, 6, 0, -14, 6, -15, 0, 5, 16, -18, 0, 0, 20, 2, 0, -24, -22, -25, 0, 12, 30, 27, 4, -33, 32, 18, 0, -37, -24, -38, 0, 24, 38, -41, 0, -5, -16, 30, 0, -48, -16, 61, 0, 30, 50, -53, 24, -55, 52, 45, 0, 74, -54, -63, 0, 33, -100, -66, 0, -69, 68, -18, 0, 80, -74, -73, 0, 2, 76, -78

Offset: 1

Author

Antti Karttunen, Dec 15 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A005187, A346237, A378756 (Dirichlet inverse).

Cf. also A294898.

Programs

PARI

A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
memoA346237 = Map();
A346237(n) = if(1==n,1,my(v); if(mapisdefined(memoA346237,n,&v), v, v = -sumdiv(n,d,if(dA005187(n/d)*A346237(d),0)); mapput(memoA346237,n,v); (v)));
A378757(n) = sumdiv(n,d,sigma(d)*A346237(n/d));

Formula

a(n) = Sum_{d|n} A000203(d)*A346237(n/d).