A379218 Möbius transform of A379108.

1, 1, 2, 2, 5, 2, 6, 4, 7, 5, 11, 4, 13, 6, 10, 8, 17, 7, 19, 10, 12, 11, 23, 8, 25, 13, 20, 12, 29, 10, 30, 16, 22, 17, 30, 14, 37, 19, 26, 20, 41, 12, 43, 22, 35, 23, 47, 16, 43, 25, 34, 26, 53, 20, 55, 24, 38, 29, 59, 20, 61, 30, 42, 32, 65, 22, 67, 34, 46, 30, 71, 28, 73, 37, 50, 38, 66, 26, 79, 40, 61, 41, 83, 24

Offset

1,3

Comments

Dirichlet convolution of A000027 with A359579.

Links

Antti Karttunen, Table of n, a(n) for n = 1..32769

Index entries for sequences related to sigma(n).

Formula

a(n) = Sum_{d|n} d*A359579(n/d).

a(n) = Sum_{d|n} A008683(d)*A379108(n/d).

Prog

(PARI)
A209229(n) = (n && !bitand(n, n-1));
A359579(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], -(1==f[k, 2]), (-A209229(1+f[k, 1]))^f[k, 2])); };
A379218(n) = sumdiv(n, d, d*A359579(n/d));

Crossrefs

Cf. A000027, A000203, A000668, A008683, A336923, A359579, A379108, A379219 (Dirichlet inverse).

Cf. also A026741.

Sequence in context: A018216 A059907 A359101 * A024931 A256612 A305797

Adjacent sequences: A379215 A379216 A379217 * A379219 A379225 A379226

Keyword

nonn,mult,new

Author

Antti Karttunen, Dec 18 2024

Status

approved