Given JSON containing data for US presidents, finds the year(s) in which the maximum number of US presidents were alive.

presidents.js

var presidents = [
  {"number":1,"president":"George Washington","birth_year":1732,"death_year":1799,"took_office":"1789-04-30","left_office":"1797-03-04","party":"No Party"},
  {"number":2,"president":"John Adams","birth_year":1735,"death_year":1826,"took_office":"1797-03-04","left_office":"1801-03-04","party":"Federalist"},
  {"number":3,"president":"Thomas Jefferson","birth_year":1743,"death_year":1826,"took_office":"1801-03-04","left_office":"1809-03-04","party":"Democratic-Republican"},
  {"number":4,"president":"James Madison","birth_year":1751,"death_year":1836,"took_office":"1809-03-04","left_office":"1817-03-04","party":"Democratic-Republican"},
  {"number":5,"president":"James Monroe","birth_year":1758,"death_year":1831,"took_office":"1817-03-04","left_office":"1825-03-04","party":"Democratic-Republican"},
  {"number":6,"president":"John Quincy Adams","birth_year":1767,"death_year":1848,"took_office":"1825-03-04","left_office":"1829-03-04","party":"Democratic-Republican"},
  {"number":7,"president":"Andrew Jackson","birth_year":1767,"death_year":1845,"took_office":"1829-03-04","left_office":"1837-03-04","party":"Democratic"},
  {"number":8,"president":"Martin Van Buren","birth_year":1782,"death_year":1862,"took_office":"1837-03-04","left_office":"1841-03-04","party":"Democratic"},
  {"number":9,"president":"William Henry Harrison","birth_year":1773,"death_year":1841,"took_office":"1841-03-04","left_office":"1841-04-04","party":"Whig"},
  {"number":10,"president":"John Tyler","birth_year":1790,"death_year":1862,"took_office":"1841-04-04","left_office":"1845-03-04","party":"Whig"},
  {"number":11,"president":"James K. Polk","birth_year":1795,"death_year":1849,"took_office":"1845-03-04","left_office":"1849-03-04","party":"Democratic"},
  {"number":12,"president":"Zachary Taylor","birth_year":1784,"death_year":1850,"took_office":"1849-03-04","left_office":"1850-07-09","party":"Whig"},
  {"number":13,"president":"Millard Fillmore","birth_year":1800,"death_year":1874,"took_office":"1850-07-09","left_office":"1853-03-04","party":"Whig"},
  {"number":14,"president":"Franklin Pierce","birth_year":1804,"death_year":1869,"took_office":"1853-03-04","left_office":"1857-03-04","party":"Democratic"},
  {"number":15,"president":"James Buchanan","birth_year":1791,"death_year":1868,"took_office":"1857-03-04","left_office":"1861-03-04","party":"Democratic"},
  {"number":16,"president":"Abraham Lincoln","birth_year":1809,"death_year":1865,"took_office":"1861-03-04","left_office":"1865-04-15","party":"Republican"},
  {"number":17,"president":"Andrew Johnson","birth_year":1808,"death_year":1875,"took_office":"1865-04-15","left_office":"1869-03-04","party":"Democratic"},
  {"number":18,"president":"Ulysses S. Grant","birth_year":1822,"death_year":1885,"took_office":"1869-03-04","left_office":"1877-03-04","party":"Republican"},
  {"number":19,"president":"Rutherford B. Hayes","birth_year":1822,"death_year":1893,"took_office":"1877-03-04","left_office":"1881-03-04","party":"Republican"},
  {"number":20,"president":"James A. Garfield","birth_year":1831,"death_year":1881,"took_office":"1881-03-04","left_office":"1881-09-19","party":"Republican"},
  {"number":21,"president":"Chester A. Arthur","birth_year":1829,"death_year":1886,"took_office":"1881-09-19","left_office":"1885-03-04","party":"Republican"},
  {"number":22,"president":"Grover Cleveland","birth_year":1837,"death_year":1908,"took_office":"1885-03-04","left_office":"1889-03-04","party":"Democratic"},
  {"number":23,"president":"Benjamin Harrison","birth_year":1833,"death_year":1901,"took_office":"1889-03-04","left_office":"1893-03-04","party":"Republican"},
  {"number":24,"president":"Grover Cleveland","birth_year":1837,"death_year":1908,"took_office":"1893-03-04","left_office":"1897-03-04","party":"Democratic"},
  {"number":25,"president":"William McKinley","birth_year":1843,"death_year":1901,"took_office":"1897-03-04","left_office":"1901-09-14","party":"Republican"},
  {"number":26,"president":"Theodore Roosevelt","birth_year":1858,"death_year":1919,"took_office":"1901-09-14","left_office":"1909-03-04","party":"Republican"},
  {"number":27,"president":"William Howard Taft","birth_year":1857,"death_year":1930,"took_office":"1909-03-04","left_office":"1913-03-04","party":"Republican"},
  {"number":28,"president":"Woodrow Wilson","birth_year":1856,"death_year":1924,"took_office":"1913-03-04","left_office":"1921-03-04","party":"Democratic"},
  {"number":29,"president":"Warren G. Harding","birth_year":1865,"death_year":1923,"took_office":"1921-03-04","left_office":"1923-08-02","party":"Republican"},
  {"number":30,"president":"Calvin Coolidge","birth_year":1872,"death_year":1933,"took_office":"1923-08-02","left_office":"1929-03-04","party":"Republican"},
  {"number":31,"president":"Herbert Hoover","birth_year":1874,"death_year":1964,"took_office":"1929-03-04","left_office":"1933-03-04","party":"Republican"},
  {"number":32,"president":"Franklin D. Roosevelt","birth_year":1882,"death_year":1945,"took_office":"1933-03-04","left_office":"1945-04-12","party":"Democratic"},
  {"number":33,"president":"Harry S. Truman","birth_year":1884,"death_year":1972,"took_office":"1945-04-12","left_office":"1953-01-20","party":"Democratic"},
  {"number":34,"president":"Dwight D. Eisenhower","birth_year":1890,"death_year":1969,"took_office":"1953-01-20","left_office":"1961-01-20","party":"Republican"},
  {"number":35,"president":"John F. Kennedy","birth_year":1917,"death_year":1963,"took_office":"1961-01-20","left_office":"1963-11-22","party":"Democratic"},
  {"number":36,"president":"Lyndon B. Johnson","birth_year":1908,"death_year":1973,"took_office":"1963-11-22","left_office":"1969-01-20","party":"Democratic"},
  {"number":37,"president":"Richard Nixon","birth_year":1913,"death_year":1994,"took_office":"1969-01-20","left_office":"1974-08-09","party":"Republican"},
  {"number":38,"president":"Gerald Ford","birth_year":1913,"death_year":2006,"took_office":"1974-08-09","left_office":"1977-01-20","party":"Republican"},
  {"number":39,"president":"Jimmy Carter","birth_year":1924,"death_year":null,"took_office":"1977-01-20","left_office":"1981-01-20","party":"Democratic"},
  {"number":40,"president":"Ronald Reagan","birth_year":1911,"death_year":2004,"took_office":"1981-01-20","left_office":"1989-01-20","party":"Republican"},
  {"number":41,"president":"George H. W. Bush","birth_year":1924,"death_year":null,"took_office":"1989-01-20","left_office":"1993-01-20","party":"Republican"},
  {"number":42,"president":"Bill Clinton","birth_year":1946,"death_year":null,"took_office":"1993-01-20","left_office":"2001-01-20","party":"Democratic"},
  {"number":43,"president":"George W. Bush","birth_year":1946,"death_year":null,"took_office":"2001-01-20","left_office":"2009-01-20","party":"Republican"},
  {"number":44,"president":"Barack Obama","birth_year":1961,"death_year":null,"took_office":"2009-01-20","left_office":null,"party":"Democratic"}
]

var years = presidents.reduce((prev, curr) => {
  var birth = curr.birth_year
  // If they are still alive, we consider them as having lived till 2016
  var death = curr.death_year === null ? 2016 : curr.death_year
  for(var index = birth; index < death; index++) {
    if (prev[index] === undefined) prev[index] = 1
    else prev[index]++
  }
  return prev
}, {})

// Find max number of presidents alive in any year
var maxAlive = Math.max.apply(null, Object.keys(years).map(year => years[year]))

var mostLivedYears = Object.keys(years)
  .filter(year => years[year] === maxAlive)

console.log(mostLivedYears)