78 (number)

78 as the sum of four distinct nonzero squares

78 is:

• the 4th discrete tri-prime; or also termed Sphenic number, and the 4th of the form (2.3.r).[1]
• an abundant number with an aliquot sum of 90.
• a semiperfect number, as a multiple of a perfect number.
• the 12th triangular number.
• a palindromic number in bases 5 (303₅), 7 (141₇), 12 (66₁₂), 25 (33₂₅), and 38 (22₃₈).
• a Harshad number in bases 3, 4, 5, 6, 7, 13 and 14.
• an Erdős–Woods number, since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member.[2]
• the dimension of the exceptional Lie group E₆ and several related objects.
• the smallest number that can be expressed as the sum of four distinct nonzero squares in more than one way: ${\displaystyle 8^{2}+3^{2}+2^{2}+1^{2}}$, ${\displaystyle 7^{2}+4^{2}+3^{2}+2^{2}}$ or ${\displaystyle 6^{2}+5^{2}+4^{2}+1^{2}}$ (see image).[3][4]

77 and 78 form a Ruth–Aaron pair.

• The atomic number of platinum.

78 is also:

• In reference to gramophone records, 78 refers those meant to be spun at 78 revolutions per minute. Compare: LP, 33+1⁄3 and 45 rpm. 33 + 45 = 78
• A typical tarot deck containing the 21 trump cards, the Fool and the 56 suit cards make up 78 cards
• The Rule of 78s is a method of yearly interest calculation
• The number used by Martin Truex Jr. and Furniture Row Racing to win the 2017 Monster Energy NASCAR Cup Series championship and 2016 Coca-Cola 600. The team and driver Regan Smith also won the 2011 Showtime Southern 500 with 78. The number is now used by owner-driver B.J. McLeod for Live Fast Motorsports.