Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3×3×3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, comprises 3 cubes whose sum of values is 42.
Forty-two is a pronic number and an abundant number; its prime factorization 2 · 3 · 7 makes it the second sphenic number and also the second of the form { 2 · 3 · r }. As with all sphenic numbers of this form, the aliquot sum is abundant by 12. 42 is also the second sphenic number to be bracketed by twin primes; 30 is also a pronic number and also rests between two primes. 42 has a 14 member aliquot sequence 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 and is itself part of the aliquot sequence commencing with the first sphenic number 30.
Further, 42 is the 10th member of the 3-aliquot tree.
42 is the product of the first three terms of Sylvester’s sequence; like the first five such numbers it is also a primary pseudoperfect number.
It is the sum of the totient function for the first eleven integers.
It is a Catalan number. Consequently; 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc.
It is the reciprocal of the sixth Bernoulli number.
42 is a Størmer number.
42 is a perfect score on the USA Math Olympiad (USAMO)[3] and International Mathematical Olympiad (IMO).[4]
In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222).
As a repeating decimal, the fraction 1?49 is a repeating decimal with a period of 42:
1?49 = 0.0204081 6326530 6122448 9795918 3673469 3877551 (42 repeating digits)
