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78 (number)

Field	Value
number	78
divisor	1, 2, 3, 6, 13, 26, 39, 78

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

In mathematics

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).
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.
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.
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: 8^2+3^2+2^2+1^2, 7^2+4^2+3^2+2^2 or 6^2+5^2+4^2+1^2 (see image).

77 and 78 form a Ruth–Aaron pair.

References

"Sloane's A007304 : Sphenic numbers". OEIS Foundation.
{{Cite OEIS. A005835. Pseudoperfect (or semiperfect) numbers n: some subset of the proper divisors of n sums to n.
"A000217 - OEIS".
{{cite OEIS. A249156
{{cite OEIS. A029957
"Sloane's A059756 : Erdős-Woods numbers". OEIS Foundation.
{{cite OEIS. A025386. Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.
{{cite OEIS. A025378. Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.

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