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42 (forty-two) is the natural number that succeeds 41 and precedes 43. ==Mathematics== * 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 . 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. * It is the third primary pseudoperfect number. * 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 an alternating sign matrix number, that is, the number of 4-by-4 alternating sign matrices. * It is the number of partitions of 10—the number of ways of expressing 10 as a sum of positive integers (note a different sense of partition from that above). * 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, is composed of 3 cubes whose sum of values is 42. * It is the third pentadecagonal number. It is a meandric number and an open meandric 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 that *: *: . *: where the infinite product is over all prime numbers, ''p''.〔J. B. Conrey & A. Ghosh, "A conjecture for the sixth power moment of the Riemann zeta-function" ''International Mathematics Research Notices'' (1998)〕〔J. B. Conrey & S. M. Gonek, "High moments of the Riemann zeta-function" ''Duke Math J.'' 107 3 (2001): 577–604〕 * 42 is a Størmer number. * 42 is the only known value that is the number of sets of four distinct positive integers a,b,c,d, each less than the value itself, such that ab-cd, ac-bd, and ad-bc are each multiples of the value. Whether there are other values remains an open question.〔(Differently Perfect – mathpages.com )〕 * 42 is a (2,6)-perfect number (super-multiperfect), as 〔(Sequence A019283 in OEIS )〕 * 42 is the resulting number of the original Smith number (4937775): Both the sum of its digits (4+9+3+7+7+7+5) and the sum of the digits in its prime factorization (3+5+5+(6+5+8+3+7)) result in 42. * The dimension of the Borel subalgebra in the exceptional Lie algebra ''e''6 is 42. * 42 is the largest number n such that there exist positive integers p,q,r with 1 - 1/n = 1/p + 1/q + 1/r * 42 is the smallest number k such that for every Riemann surface C, #Aut(C) <= k deg(KC) = k (2g -2) (Hurwitz's automorphisms theorem) * In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222). * 42 is a perfect score on the USA Math Olympiad (USAMO)〔(Alex Zhai ties for second-highest score in 2007 USA Mathematical Olympiad ) – By Andrew Lovdahl Gargoyle staff reporter Posted Monday, May 7, 2007, The OG, news & student awards – Online Gargoyle〕 and International Mathematical Olympiad (IMO).〔CBC News staff, "(Canadian math champ's skills add up to a perfect score )" CBC News July 20, 2004. "A 16-year-old Canadian was one of four students who achieved a perfect score at an international mathematics competition. Jacob Tsimerman of Toronto scored 42 out of 42, making him one of 45 individual gold medallists at the 45th International Mathematical Olympiad in Athens."〕 * 42 is the maximum of core points awarded in International Baccalaureate Diploma Programme. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「42 (number)」の詳細全文を読む スポンサード リンク
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