240 (number)

240 (two hundred forty) is the natural number following 239 and preceding 241.

Mathematics

240 is a pronic number, since it can be expressed as the product of two consecutive integers, 15 and 16. It is a semiperfect number, equal to the concatenation of two of its proper divisors (24 and 40).

It is also a highly composite number with 20 divisors in total, more than any smaller number; and a refactorable number or tau number, since one of its divisors is 20, which divides 240 evenly.

240 is the aliquot sum of only two numbers: 120 and 57121 (or 239²); and is part of the 12161-aliquot tree that goes: 120, 240, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 0.

It is the smallest number that can be expressed as a sum of consecutive primes in three different ways:

$${\displaystyle {\begin{aligned}240&=113+127\\240&=53+59+61+67\\240&=17+19+23+29+31+37+41+43\\\end{aligned}}}$$

240 is highly totient, since it has thirty-one totient answers, more than any previous integer.

It is palindromic in bases 19 (CC₁₉), 23 (AA₂₃), 29 (88₂₉), 39 (66₃₉), 47 (55₄₇) and 59 (44₅₉), while a Harshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15 (and 73 other bases).

240 is the algebraic polynomial degree of sixteen-cycle logistic map, ${\displaystyle r_{16}.}$

240 is the number of distinct solutions of the Soma cube puzzle.

There are exactly 240 visible pieces of what would be a four-dimensional version of the Rubik's Revenge — a ${\displaystyle 4\times 4\times 4}$ Rubik's Cube. A Rubik's Revenge in three dimensions has 56 (64 – 8) visible pieces, which means a Rubik's Revenge in four dimensions has 240 (256 – 16) visible pieces.

E₈ has 240 roots.

References