Arithmetic properties of 2color overpartition pairs
M. S. M. Naika, S. S. Nayaka
Let p_{k,2}(n) counts the number of overpartition pairs of n with
2color in which one of the colors appears only in parts
that are multiples of k. We establish several infinite families of congruences modulo powers of 2 and 3 for
p_{k,2}(n)
where k= 2 and 3. For example, for all n ≥ 0 and α ≥ 0,
we have
p_{2,2}(16 · 3^{4α+2}n + 34 · 3^{4α+1}) ≡ 0 (mod 128),
p_{3,2}(6 · 25^{α+2}n + 20·25^{α+2}) ≡ 0 (mod 27).
Tbilisi Mathematical Journal, Vol. 13(2) (2020), pp. 6785
