1441440

Appears in sequences

• Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.at n=39A002182
• 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=10A002201
• 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=31A004394
• 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=10A004490
• Where records occur in A038548.at n=36A004778
• Number of self-dual Boolean functions of n variables with transitive symmetry group.at n=10A008841
• Numbers k such that sigma(k)/phi(k) sets a new record.at n=29A018894
• Floor( n(n+1)(n+2)...(n+7) / (n+(n+1)+(n+2)+...+(n+7)) ).at n=7A032777
• Integer quotients n(n+1)(n+2)...(n+7) / (n+(n+1)+(n+2)+...+(n+7)).at n=3A032779
• a(n) is the minimal number of binary order n which has maximal number of divisors in this interval.at n=21A036484
• Least common multiple of {2, 4, 6, ..., 2n}.at n=15A051426
• a(n) = (4*n+6)(!^4)/6(!^4).at n=5A051618
• a(n) is the smallest number which has n consecutive divisors k, k+1, ..., k+n-1 such that the quotients all begin with the same digit.at n=6A053014
• Consider the subsets of proper divisors of a number that sum to the number. These are numbers that set a record number of such subsets.at n=38A065218
• Numbers k that are repdigits in more bases (smaller than k) than any smaller number.at n=38A066044
• Triangle T(n,k) defined by Sum_{1<=k<=n} T(n,k)*u^k*t^n/n! = exp(((1-t)*(1-t^2)*(1-t^3)...)^(-u)-1).at n=32A066045
• LCM of numbers <= n and having a factor in common with n.at n=31A066574
• LCM of numbers m such that 1 <= m <= n, m has a common factor with n, but m does not divide n.at n=33A066575
• Least k such that n*prime(k) <= k*tau(k).at n=17A073066
• Least k such that n*prime(k) <= k*tau(k).at n=16A073066