A337931 Number of ways to write n as the sum of two positive integers, s,t such that phi(s) is not equal to phi(t), where phi is the Euler totient function (A000010).

0, 0, 0, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5, 6, 6, 6, 7, 7, 9, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 14, 14, 15, 15, 16, 16, 18, 18, 17, 18, 19, 20, 21, 20, 21, 20, 22, 23, 21, 23, 24, 25, 26, 24, 26, 27, 25, 27, 29, 29, 30, 29, 30, 30, 30, 31, 33, 32, 32, 33, 35, 34, 35, 34, 36, 37

Offset

1,5

Links

Table of n, a(n) for n=1..76.

Formula

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

Mathematica

Table[Sum[1 - KroneckerDelta[EulerPhi[i], EulerPhi[n - i]], {i, Floor[n/2]}], {n, 100}]

Crossrefs

Cf. A000010, A337930.

Sequence in context: A285582 A032562 A076973 * A008649 A008650 A062051

Adjacent sequences: A337928 A337929 A337930 * A337932 A337933 A337934

Keyword

nonn

Author

Wesley Ivan Hurt, Sep 30 2020

Status

approved