A337930 Number of ways to write n as the sum of two positive integers s,t such that s <= t and phi(s) = phi(t) where phi is the Euler totient function (A000010).

0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 2, 0, 1, 2, 2, 1, 1, 0, 2, 1, 3, 1, 1, 3, 2, 1, 1, 0, 3, 1, 1, 3, 2, 0, 1, 0, 2, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2, 1, 3, 1, 1, 2, 2, 0, 3, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 3, 4, 1, 4

Offset

1,10

Links

Table of n, a(n) for n=1..94.

Formula

a(n) = Sum_{i=1..floor(n/2)} [phi(i) = phi(n-i)], where phi is the Euler totient function (A000010) and [ ] is the Iverson bracket.

Example

a(10) = 2; 10 = 6 + 4 and phi(6) = phi(4), 10 = 5 + 5 and phi(5) = phi(5).

Mathematica

Table[Sum[KroneckerDelta[EulerPhi[i], EulerPhi[n - i]], {i, Floor[n/2]}], {n, 100}]

Crossrefs

Cf. A000010, A337931.

Sequence in context: A005087 A050332 A369258 * A340691 A216658 A214020

Adjacent sequences: A337927 A337928 A337929 * A337931 A337932 A337933

Keyword

nonn

Author

Wesley Ivan Hurt, Sep 30 2020

Status

approved