30 (number) - in Mathematics

In Mathematics

30 is the sum of the first four squares, which makes it a square pyramidal number.

It is a primorial and is the smallest Giuga number.

30 is the smallest sphenic number, and the smallest of the form where r is a prime greater than 3. 30 has an aliquot sum of 42; the second sphenic number and all sphenic numbers of this form have an aliquot sum 12 greater than themselves. The aliquot sequence of 30 is 16 members long, it comprises (30,42,54,66,78,90,144,259,45,33,15,9,4,3,1,0)

Thirty has but one number for which it is the aliquot sum: the square number 841.

Adding up some subsets of its divisors (e.g., 5, 10 and 15) gives 30, hence 30 is a semiperfect number.

30 is the largest number such that all coprimes smaller than itself, except for 1, are prime.

A polygon with thirty sides is called a tricontagon.

The icosahedron and the dodecahedron are Platonic solids with 30 edges. The icosidodecahedron is an Archimedean solid with 30 vertices, and the Tutte–Coxeter graph is a symmetric graph with 30 vertices.

E₈ has Coxeter number 30.

30 is a Harshad number.

Since any group G such that |G| = pnm, where p does not divide m, has a subgroup of order pn, and 30 is the only number less than 60 that is not either a prime or of the above form, it is the only candidate for the order of a simple group less than 60 that one needs other methods to reject.