55440

Appears in sequences

• a(n) = n!/6!.at n=5A001730
• Expansion of reciprocal of theta series of E_8 lattice.at n=2A001943
• Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.at n=27A002182
• 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=8A002201
• Denominators of Cauchy numbers of second type (= Bernoulli numbers B_n^{(n)}).at n=43A002790
• 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=23A004394
• 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=8A004490
• Where records occur in A038548.at n=24A004778
• Maximal period of an n-stage shift register.at n=17A005417
• Denominators of Cauchy numbers of first type.at n=43A006233
• Number of planar embedded labeled trees with n nodes: (2*n-3)!/(n-1)! for n >= 2, a(1) = 1.at n=6A006963
• Theta series of A_7 lattice.at n=14A008447
• Coordination sequence for 4-dimensional I-centered cubic orthogonal lattice.at n=24A008532
• Numbers k such that sigma(k)/phi(k) sets a new record.at n=22A018894
• a(1)=1; for n > 1, a(n) is the smallest number with the same number of divisors as 2*a(n-1).at n=18A019505
• Numbers k such that sigma(k) >= 4*k.at n=4A023198
• Least common multiple of the first n composite numbers.at n=13A025543
• Least common multiple of the first n composite numbers.at n=14A025543
• a(n) = 7*(n+1)*binomial(n+3,7).at n=5A027792
• a(n) = 14*(n+1)*binomial(n+5,8).at n=4A027813