A337930 - OEIS

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

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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