A345745 a(n) = Sum_{k=1..n} n^(1 - mu(k)^2).

1, 2, 3, 7, 9, 11, 13, 22, 33, 37, 41, 56, 61, 66, 71, 91, 97, 120, 127, 153, 161, 169, 177, 208, 241, 251, 287, 325, 337, 349, 361, 404, 417, 430, 443, 491, 505, 519, 533, 586, 601, 616, 631, 689, 749, 766, 783, 847, 913, 981, 1001, 1072, 1093, 1167, 1189, 1266, 1289, 1312

Offset

1,2

Comments

For all k <= n, add 1 if k is squarefree, otherwise add n. For n = 12, the 8 squarefree numbers less than or equal to 12 are 1, 2, 3, 5, 6, 7, 10, and 11. This leaves 4 numbers that are not squarefree, which gives a(12) = 8 + 4*12 = 56.

Links

Table of n, a(n) for n=1..58.

Mathematica

Table[Sum[n^(1 - MoebiusMu[k]^2), {k, n}], {n, 80}]

Prog

(PARI) a(n) = sum(k=1, n, if (issquarefree(k), 1, n)); \\ Michel Marcus, Jun 26 2021

Crossrefs

Cf. A008683 (mu), A345743.

Sequence in context: A279064 A294109 A294263 * A280110 A203234 A212985

Adjacent sequences: A345742 A345743 A345744 * A345746 A345747 A345748

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 25 2021

Status

approved