720720

Appears in sequences

• Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.at n=37A002182
• Superior highly composite numbers: positive integers n for which there is an e > 0 such that d(n)/n^e >= d(k)/k^e for all k > 1, where the function d(n) counts the divisors of n (A000005).at n=9A002201
• a(n) = denominator of harmonic number H(n) = Sum_{i=1..n} 1/i.at n=15A002805
• a(n) = LCM(1,2,...,n) / n.at n=16A002944
• Largest number divisible by all numbers < its n-th root.at n=4A003102
• Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1.at n=16A003418
• Binomial coefficient C(6n,n-7).at n=4A004362
• Superabundant [or super-abundant] numbers: n such that sigma(n)/n > sigma(m)/m for all m < n, sigma(n) being A000203(n), the sum of the divisors of n.at n=30A004394
• Colossally abundant numbers: m for which there is a positive exponent epsilon such that sigma(m)/m^{1 + epsilon} >= sigma(k)/k^{1 + epsilon} for all k > 1, so that m attains the maximum value of sigma(m)/m^{1 + epsilon}.at n=9A004490
• Where records occur in A038548.at n=34A004778
• Maximal period of an n-stage shift register.at n=23A005417
• Maximal period of an n-stage shift register.at n=24A005417
• Triangle of coefficients of Legendre polynomials 2^n P_n (x).at n=39A008556
• Binomial coefficients C(n,62).at n=4A017726
• Binomial coefficients C(66,n).at n=4A017782
• Numbers k such that sigma(k)/phi(k) sets a new record.at n=28A018894
• Least highly composite number divisible by n.at n=12A022404
• Least highly composite number divisible by n.at n=25A022404
• a(n) = LCM{1, C(n-1,1), C(n-2,2), ..., C(n-[ n/2 ],[ n/2 ])}.at n=16A025560
• Denominator of n * n-th harmonic number.at n=16A027611