Cuarenta y Dos
Quote:
Originally Posted by Zunaid
As always the answer is:
42

Right you are ZBhai. Great to hear from you again. Whatever happened to Deep Thought? Still in Magrathea you reckon? Now more deliberately misleading factoids on that pseudoperfect number.
Quote:
42 (fortytwo) is the natural number following 41 and preceding 43.
It is a composite number; its factorization 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 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 3aliquot tree.
42 is the product of the first three terms of Sylvester's sequence; like the first four 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.
It is the reciprocal of a Bernoulli number
It is conjectured to be the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function". In particular, Conrey & Ghosh have conjectured
where the infinite product is over all prime numbers, p.
It is a pronic number, and the third 15gonal number. It is a meandric number and an open meandric number.
42 is a perfect score on the USA Math Olympiad (USAMO) and International Mathematical Olympiad (IMO).
In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222).
The eight digits of pi beginning from 242,422 places after the decimal point are 42424242.
The first digit (4) taken to the power of the second digit (2) is equal to the second digit (2) taken to the power of the first digit (4): 42 = 24 = 16. It follows clearly that 24 exhibits the same characteristic, and in fact 24 is the only other twodigit nonrepdigit number that does. (All twodigit repdigit numbers exhibit this characteristic.)
Link:http://en.wikipedia.org/wiki/42_%28number%29

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Last edited by Sohel; August 23, 2007 at 12:35 PM..
