```ts
/**
 * Generates a backoff schedule for dialing a flaky endpoint.
 * @param base - The initial idle time before the second dial.
 * @param factor - The multiplication factor for each subsequent idle.
 * @param cap - The maximum idle time allowed.
 * @param attempts - The number of dial attempts to schedule.
 * @returns An array of moments when each dial should occur.
 */
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 not smaller than base.');
  if (!Number.isInteger(attempts) || attempts < 1) throw new Error('Attempts must be a whole number of one or more.');

  const schedule: number[] = [0];
  let nextIdle = base;

  for (let i = 1; i < attempts; i++) {
    schedule.push(schedule[i - 1] + nextIdle);
    nextIdle = Math.min(nextIdle * factor, cap);
  }

  return schedule;
}
```