A341062 Sequence whose partial sums give A000005.

1, 1, 0, 1, -1, 2, -2, 2, -1, 1, -2, 4, -4, 2, 0, 1, -3, 4, -4, 4, -2, 0, -2, 6, -5, 1, 0, 2, -4, 6, -6, 4, -2, 0, 0, 5, -7, 2, 0, 4, -6, 6, -6, 4, 0, -2, -2, 8, -7, 3, -2, 2, -4, 6, -4, 4, -4, 0, -2, 10, -10, 2, 2, 1, -3, 4, -6, 4, -2, 4, -6, 10, -10, 2, 2, 0, -2, 4, -6, 8, -5, -1, -2, 10, -8, 0, 0, 4, -6, 10

Offset: 1

Author

Omar E. Pol, Feb 04 2021

Keywords

• sign
• easy

Comments

Essentially a duplicate of A051950.

Convolved with A000041 gives A138137.

Convolved with A000027 gives the nonzero terms of A006218.

Convolved with A000070 gives the nonzero terms of A006128.

Convolved with A014153 gives the nonzero terms of A284870.

Convolved with A036469 gives the nonzero terms of A305082.

Convolved with the nonzero terms of A006218 gives A055507.

Convolved with the nonzero terms of A000217 gives the nonzero terms of A078567.

Crossrefs

1 together with A051950.

Cf. A000005 (partial sums).

Cf. A000027, A000041, A000070, A000217, A006128, A006218, A014153, A036469, A055507, A078567, A138137, A284870, A305082, A340793.

Programs

Mathematica

Join[{1}, Differences[Table[DivisorSigma[0, n], {n, 1, 90}]]] (* Amiram Eldar, Feb 06 2021 *)

Formula

a(n) = A051950(n) for n > 1.