A369189 Sum of the squarefree triangular divisors of n.

1, 1, 4, 1, 1, 10, 1, 1, 4, 11, 1, 10, 1, 1, 19, 1, 1, 10, 1, 11, 25, 1, 1, 10, 1, 1, 4, 1, 1, 35, 1, 1, 4, 1, 1, 10, 1, 1, 4, 11, 1, 31, 1, 1, 19, 1, 1, 10, 1, 11, 4, 1, 1, 10, 56, 1, 4, 1, 1, 35, 1, 1, 25, 1, 1, 76, 1, 1, 4, 11, 1, 10, 1, 1, 19, 1, 1, 88, 1, 11, 4

Offset

1,3

Comments

Inverse Möbius transform of n * mu(n)^2 * c(n), where c(n) is the characteristic function of triangular numbers (A010054). - Wesley Ivan Hurt, Jun 21 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = Sum_{d|n} d * mu(d)^2 * c(d), where c = A010054.

Mathematica

Table[Sum[d*MoebiusMu[d]^2 (Floor[Sqrt[2 d + 1] + 1/2] - Floor[Sqrt[2 d] + 1/2]), {d, Divisors[n]}], {n, 100}]

Prog

(PARI) a(n) = sumdiv(n, d, if (issquarefree(d) && ispolygonal(d, 3), d)); \\ Michel Marcus, Jan 16 2024

Crossrefs

Cf. A008683 (mu), A008966, A010054, A061304 (squarefree triangular numbers), A369188.

Sequence in context: A056647 A056057 A226234 * A185027 A016520 A361731

Adjacent sequences: A369186 A369187 A369188 * A369190 A369191 A369192

Keyword

nonn,easy,changed

Author

Wesley Ivan Hurt, Jan 15 2024

Status

approved