78 (number)
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Template:Refimprove Template:Infobox number 78 (seventy-eight) is the natural number following 77 and preceding 79.
In mathematics
78 is:
- the 5th discrete tri-prime; or also termed Sphenic number, and the 4th of the form (2.3.r).<ref>{{#invoke:citation/CS1|citation
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- 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.<ref>Template:Cite OEIS</ref>
- the 12th triangular number.<ref>{{#invoke:citation/CS1|citation
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- a palindromic number in bases 5 (3035), 7 (1417),<ref>Template:Cite OEIS</ref> 12 (6612),<ref>Template:Cite OEIS</ref> 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.<ref>{{#invoke:citation/CS1|citation
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- 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: <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>Template:Cite OEIS</ref><ref>Template:Cite OEIS</ref>
77 and 78 form a Ruth–Aaron pair.
References
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