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78 (number)

Natural number From Wikipedia, the free encyclopedia

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78 (seventy-eight) is the natural number following 77 and preceding 79.

Quick Facts ← 77 78 79 →, Cardinal ...
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In mathematics

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78 as the sum of four distinct nonzero squares

78 is:

  • the 5th 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; within an aliquot sequence of nine composite numbers (78, 90,144,259,45,33,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
  • a semiperfect number, as a multiple of a perfect number.[2]
  • the 12th triangular number.[3]
  • a palindromic number in bases 5 (3035), 7 (1417),[4] 12 (6612),[5] 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.[6]
  • 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: , or (see image).[7][8]

77 and 78 form a Ruth–Aaron pair.

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References

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