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Old August 23, 2007, 12:00 PM
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Sohel Sohel is offline
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Originally Posted by Zunaid
As always the answer is:

Right you are Z-Bhai. 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.

42 (forty-two) 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 3-aliquot 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 15-gonal 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 two-digit non-repdigit number that does. (All two-digit repdigit numbers exhibit this characteristic.)

"And do not curse those who call on other than GOD, lest they blaspheme and curse GOD, out of ignorance. We have adorned the works of every group in their eyes. Ultimately, they return to their Lord, then He informs them of everything they had done." (Qur'an 6:108)

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