```ts
export function backoffSchedule(base: number, factor: number, cap: number, attempts: number): number[] {
  if (!Number.isInteger(base) || base < 1) throw new Error('Base must be a whole number of one or more');
  if (!Number.isInteger(factor) || factor < 1) throw new Error('Factor must be a whole number of one or more');
  if (!Number.isInteger(cap) || cap < base) throw new Error('Cap must be a whole number and not smaller than base');
  if (!Number.isInteger(attempts) || attempts < 1) throw new Error('Attempts must be a whole number of one or more');

  const result: number[] = [];
  let idleTime = base;

  for (let i = 0; i < attempts; i++) {
    result.push(result.length === 0 ? 0 : result[i - 1] + idleTime);
    idleTime = Math.min(idleTime * factor, cap);
  }

  return result;
}
```