31080

Appears in sequences

• a(1)=1, a(2)=2, a(3)=3; for n >= 3, a(n) is smallest number such that all a(i) for 1 <= i <= n are distinct, all a(i)+a(j) for 1 <= i < j <= n are distinct and all a(i)+a(j)+a(k) for 1 <= i < j < k <= n are distinct.at n=27A036241
• Numbers that can be expressed as the difference of the squares of primes in exactly six distinct ways.at n=19A092002
• Least number beginning with n such that every partial sum is a square.at n=30A095158
• Refines A075197(n): number of partitions of n balls of n colors. The refinement has shape A000041(n).at n=39A130273
• Triangle read by rows: T(n,k) is the number of paths in the right half-plane, from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0), having k U steps (0 <= k <= floor(n/2)).at n=39A132886
• Averages of twin primes such that the sum of the lower, average and upper parts of the twin primes are averages of other twin primes.at n=13A132929
• a(n) = 1728*n - 24.at n=17A157287
• Multiples of 840.at n=37A169827
• Numbers with exactly 64 divisors.at n=36A172443
• Triangle read by rows: T(n,k) is the number of weighted lattice paths in L_n having k (1,1)-steps. L_n is the set of lattice paths of weight n that start at (0,0) and end on the horizontal axis and whose steps are of the following four kinds: a (1,0)-step with weight 1; a (1,0)-step with weight 2; a (1,1)-step with weight 2; a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.at n=43A182880
• Table of coefficients of a polynomial sequence of binomial type related to the enumeration of minimax trees A080795.at n=32A185419
• Numbers with prime factorization pqrst^3.at n=16A189984
• Triangle of coefficients of a sequence of binomial type polynomials.at n=23A195204
• Number of -n..n arrays of 4 elements with zero sum and no two neighbors summing to zero.at n=17A199833
• a(n) = 2*n*(n+1)*(n+2)/3.at n=35A210440
• Numbers n such that {largest m such that 1, 2, ..., m divide n} is different from {largest m such that m! divides n^2}.at n=18A232099
• Numbers k such that k is the average of four consecutive primes k-11, k-1, k+1 and k+11.at n=30A259025
• Numbers n such that the multiplicative group modulo n is the direct product of 6 cyclic groups.at n=18A272596
• Positive integers that are square roots of products a*(a+d)*(a+2*d) with coprime a > 0, d >= 0.at n=12A284876
• T(n,k) is (1/n) times the n-th derivative of the difference between the k-th tetration of x (power tower of order k) and its predecessor at x=1; triangle T(n,k), n>=1, 1<=k<=n, read by rows.at n=33A295027