Would a solution involving hashmaps and recursion not also be valid?

let happyMap = {};

function happyNumber(number) {

if (happyMap[number] != undefined) return false;

reduction = number.toString().split("").map(x => parseInt(x)**2).reduce((acc, current, index) => { return acc + current; }, 0);

happyMap[number] = reduction;

if (reduction == 1) return true;

return happyNumber(reduction);

}