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78 (number)

From Wikipedia, the free encyclopedia
← 77 78 79 →
Cardinalseventy-eight
Ordinal78th
(seventy-eighth)
Factorization2 × 3 × 13
Divisors1, 2, 3, 6, 13, 26, 39, 78
Greek numeralΟΗ´
Roman numeralLXXVIII
Binary10011102
Ternary22203
Senary2106
Octal1168
Duodecimal6612
Hexadecimal4E16

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

In mathematics

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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 33; 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.
  • 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: , or (see image).[3][4]

77 and 78 form a Ruth–Aaron pair.

In science

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In other fields

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78 is also:

References

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  1. ^ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  2. ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A025386 (Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A025378 (Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.