A362806 Number of numbers k, 1 <= k <= n, such that mu(k) = mu(n-k+1).

1, 0, 1, 2, 1, 4, 3, 2, 3, 2, 5, 4, 3, 4, 11, 2, 5, 2, 11, 6, 9, 2, 13, 6, 7, 6, 13, 6, 9, 6, 17, 8, 13, 8, 27, 8, 5, 8, 21, 10, 11, 12, 23, 14, 9, 12, 29, 18, 13, 2, 27, 16, 21, 10, 27, 12, 17, 14, 35, 24, 11, 12, 29, 16, 23, 14, 33, 16, 23, 16, 53, 26, 19, 16, 35, 24, 25, 22

Offset

1,4

Links

Table of n, a(n) for n=1..78.

Formula

a(n) = Sum_{k=1..n} [mu(k) = mu(n-k+1)], where mu is the Möbius function (A008683) and [ ] is the Iverson bracket.

Example

a(6) = 4; for n=6 and k=1,2,5,6 we have mu(1) = 1 = mu(6-1+1), mu(2) = -1 = mu(6-2+1), mu(5) = -1 = mu(6-5+1), mu(6) = 1 = mu(6-6+1).

Mathematica

Table[Sum[KroneckerDelta[MoebiusMu[n - k + 1], MoebiusMu[k]], {k, n}], {n, 100}]

Prog

(PARI) a(n) = sum(k=1, n, moebius(k) == moebius(n-k+1)); \\ Michel Marcus, May 04 2023

Crossrefs

Cf. A008683 (mu).

Sequence in context: A347820 A318569 A336280 * A277749 A227629 A183201

Adjacent sequences: A362803 A362804 A362805 * A362807 A362808 A362809

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 04 2023

Status

approved