A362719 Number of numbers k, 1 <= k <= n, such that phi(k) = phi(n-k+1).

1, 2, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 2, 3, 2, 1, 2, 1, 2, 1, 0, 1, 2, 3, 2, 3, 2, 3, 0, 1, 4, 3, 2, 1, 0, 3, 2, 5, 2, 1, 6, 3, 2, 1, 0, 5, 2, 1, 6, 3, 0, 1, 0, 3, 2, 3, 4, 3, 0, 3, 4, 3, 0, 3, 2, 5, 2, 1, 4, 3, 0, 5, 2, 3, 2, 3, 0, 1, 4, 3, 0, 1, 6, 7, 2, 7, 2, 3

Offset

1,2

Links

Table of n, a(n) for n=1..95.

Formula

a(n) = Sum_{k=1..n} [phi(k) = phi(n-k+1)], where phi is the Euler phi function (A000010) and [ ] is the Iverson bracket.

Example

a(9) = 3, since phi(4) = phi(9-4+1), phi(5) = phi(9-5+1), and phi(6) = phi(9-6+1).

Mathematica

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

Prog

(PARI) a(n) = sum(k=1, n, eulerphi(k) == eulerphi(n-k+1)); \\ Michel Marcus, May 01 2023

Crossrefs

Cf. A000010 (phi).

Sequence in context: A366074 A293439 A144095 * A076092 A080468 A321863

Adjacent sequences: A362716 A362717 A362718 * A362720 A362721 A362722

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 30 2023

Status

approved