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

1,5

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)

Formula

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

Prog

(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(d<n, A005187(n/d)*A346237(d), 0)); mapput(memoA346237, n, v); (v)));
A378757(n) = sumdiv(n, d, sigma(d)*A346237(n/d));

Crossrefs

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

Cf. also A294898.

Sequence in context: A213081 A127446 A046157 * A378756 A035167 A071448

Adjacent sequences: A378754 A378755 A378756 * A378758 A378759 A378760

Keyword

sign

Author

Antti Karttunen, Dec 15 2024

Status

approved