4324320

Appears in sequences

• 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=11A002201
• Denominator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.at n=31A002444
• 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=34A004394
• 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=11A004490
• Numbers k such that sigma(k)/phi(k) sets a new record.at n=33A018894
• 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=25A019505
• a(n) = (4*n+10)(!^4)/10(!^4), related to A000407 ((4*n+2)(!^4) quartic, or 4-factorials).at n=5A051622
• Number of permutations of n letters where exactly 5 change position.at n=27A060836
• Smallest number whose square is divisible by n!.at n=13A065887
• Maximal degree of an irreducible representation of the group of n X n signed permutation matrices.at n=13A066051
• Least k such that n*prime(k) <= k*tau(k).at n=21A073066
• Numbers k such that sigma(k)/k >= sigma(m)/m for all m <= k.at n=35A077006
• Smallest numbers having exactly n divisors d>1 such that also d+1 is a divisor.at n=31A088726
• Minimal numbers having in canonical prime factorization at least one factor p^e such that e+1 is not prime, p prime and e>0.at n=25A099317
• a(1) = 1. For n >= 2, a(n) = sum of the two (not necessarily distinct) earlier terms, a(j) and a(k), which maximizes d(a(j)+a(k)), where d(m) is the number of positive divisors of m. a(n) = the minimum (a(j)+a(k)) if more than one such sum has the maximum number of divisors.at n=28A115387
• Numbers n such that n^12 + 488669 is prime.at n=18A122131
• Terms in A005179 where prime signature differs from that of corresponding term in A038547.at n=26A122813
• Triangle read by rows: T(n,d) = (n!/d!)*(n+1)*binomial(2n-d+1,n+1)/(n-d+1) (0 <= d <= n).at n=30A123225
• Smallest number m having exactly n divisors d with sqrt(m/2) <= d < sqrt(2*m).at n=36A128605
• Numbers k meeting the following criterion: if k is a multiple of d, then it is also a multiple of the smallest number with same number of divisors as d.at n=25A134865