78 (number)

Source: 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 followed by 79.

In mathematics

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
    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

In other fields

78 is also:

  • In reference to
    45
    rpm. 33 + 45 = 78
  • A typical
    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
    B.J. McLeod for Live Fast Motorsports
    .

References

  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.