This gist has two methods that convert between integer and its base 62 equivalent.

toAndFromBase62ToInt.js

function toBase62(number, arr){
    var list = [0,1,2,3,4,5,6,7,8,9,'a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z','A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z'];
	
	if(!arguments.length)
		throw new SyntaxError("toBase62: Invalid syntax. Use toBase62(number[, Array])");
	
	number = parseInt(arguments[0], 10);
	
	if(isNaN(number))
		throw new TypeError("toBase62: First parameter needs to be a valid integer number");
	
	if(number<0){
		console.error("toBase62: Number passed is less than zero");
		console.error("toBase62: Taking its abs and moving on");
		number = Math.abs(number);
	}
	
	var q = Math.floor(number / 62), r = number % 62;
	
	if (!(arguments[1] instanceof Array))
		arr = arguments[1] = [];
	
	/* arguments[2] is used internally for some book keeping */
	if (!arguments[2])
		arguments[2]=0;
	
	if(arguments[2]===0 && arguments[1].length>0)
		arr = arguments[1] = [];
	
	if ( q === 0){
		arr.push(list[r]);
		return arr.reverse().join("");
	}
	else {
		q = Math.floor(number / 62);
		r = number % 62;
		arr.push(list[r]);
		return toBase62(q, arr,++arguments[2]);
	}
}

function fromBase62ToInt(base62num){
	
	if(!arguments.length || (typeof arguments[0] !== "string"))
			throw new SyntaxError("fromBase62ToInt: Invalid syntax. Use fromBase62ToInt(String)");
			
	var list = {
					0: 0,
					1: 1,
					2: 2,
					3: 3,
					4: 4,
					5: 5,
					6: 6,
					7: 7,
					8: 8,
					9: 9,
					a: 10,
					b: 11,
					c: 12,
					d: 13,
					e: 14,
					f: 15,
					g: 16,
					h: 17,
					i: 18,
					j: 19,
					k: 20,
					l: 21,
					m: 22,
					n: 23,
					o: 24,
					p: 25,
					q: 26,
					r: 27,
					s: 28,
					t: 29,
					u: 30,
					v: 31,
					w: 32,
					x: 33,
					y: 34,
					z: 35,
					A: 36,
					B: 37,
					C: 38,
					D: 39,
					E: 40,
					F: 41,
					G: 42,
					H: 43,
					I: 44,
					J: 45,
					K: 46,
					L: 47,
					M: 48,
					N: 49,
					O: 50,
					P: 51,
					Q: 52,
					R: 53,
					S: 54,
					T: 55,
					U: 56,
					V: 57,
					W: 58,
					X: 59,
					Y: 60,
					Z: 61
				},
		numArray = base62num.split("").reverse(),
		intNum = 0;
		
		for (var i = 0; i < numArray.length; i++){
			intNum += list[numArray[i]]*(Math.pow(62,i));
		}
		
		return intNum;
}