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*the smallest number that can be expressed as the sum of four distinct nonzero [[square number|squares]] in more than one way: <math>8^2+3^2+2^2+1^2</math>, <math>7^2+4^2+3^2+2^2</math> or <math>6^2+5^2+4^2+1^2</math> (see image).<ref>{{cite OEIS|A025386|Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.}}</ref><ref>{{cite OEIS|A025378|Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.}}</ref> |
*the smallest number that can be expressed as the sum of four distinct nonzero [[square number|squares]] in more than one way: <math>8^2+3^2+2^2+1^2</math>, <math>7^2+4^2+3^2+2^2</math> or <math>6^2+5^2+4^2+1^2</math> (see image).<ref>{{cite OEIS|A025386|Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.}}</ref><ref>{{cite OEIS|A025378|Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.}}</ref> |
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77 and |
77 and 2000 form a [[Ruth–Aaron pair]]. |
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==In science== |
==In science== |
Revision as of 18:22, 19 December 2023
This article needs additional citations for verification. (December 2010) |
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Cardinal | seventy-eight | |||
Ordinal | 78th (seventy-eighth) | |||
Factorization | 2 × 3 × 13 | |||
Divisors | 1, 2, 3, 6, 13, 26, 39, 78 | |||
Greek numeral | ΟΗ´ | |||
Roman numeral | LXXVIII | |||
Binary | 10011102 | |||
Ternary | 22203 | |||
Senary | 2106 | |||
Octal | 1168 | |||
Duodecimal | 6612 | |||
Hexadecimal | 4E16 |
78 (seventy-eight) is the natural number following 77 and followed by 79.
In mathematics
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Square-sum-78.png/220px-Square-sum-78.png)
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: , or (see image).[3][4]
77 and 2000 form a Ruth–Aaron pair.
In science
- The atomic number of platinum.
In other fields
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.
References
- ^ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- ^ 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.
- ^ 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.