A378756 Dirichlet convolution of A046692 and A005187, where A046692 is the Dirichlet inverse of sigma.

1, 0, 0, 0, 2, -2, 3, 0, 3, -6, 7, 0, 9, -8, -6, 0, 14, -6, 15, 0, -5, -16, 18, 0, 4, -20, -2, 0, 24, 14, 25, 0, -12, -30, -15, 0, 33, -32, -18, 0, 37, 12, 38, 0, -12, -38, 41, 0, 14, -8, -30, 0, 48, 4, -33, 0, -30, -50, 53, 0, 55, -52, -27, 0, -38, 26, 63, 0, -33, 32, 66, 0, 69, -68, -6, 0, -38, 38, 73, 0, 7, -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. A005187, A046692, A378757 (Dirichlet inverse).

Cf. also A294898.

Programs

PARI

A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A046692(n) = { my(f=factor(n)~); prod(i=1, #f, if(1==f[2,i], -(f[1,i]+1), if(2==f[2,i], f[1,i], 0))); };
A378756(n) = sumdiv(n,d,A046692(d)*A005187(n/d));

Formula

a(n) = Sum_{d|n} A046692(d)*A005187(n/d).