Infinite families of arithmetic identities and congruences for bipartitions with 3-cores

Let A3(n)A3(n) denote the number of bipartitions of n   that are 3-cores. By employing Ramanujan's simple theta function identities, we prove that A3(2n+1)=13 σ(6n+5), where σ(n)σ(n) denotes the sum of the positive divisors of n  . We also find several infinite families of arithmetic identities and congruences for A3(n)A3(n), which include generalizations of some recent results on A3(n)A3(n) by B.L.S. Lin (2014) [6].