Sequences

Number of partitions of n into parts of 13 kinds.

Number of partitions of n into parts of 14 kinds.

Number of partitions of n into parts of 15 kinds.

Number of partitions of n into parts of 16 kinds.

Number of partitions of n into parts of 17 kinds.

Number of partitions of n into parts of 18 kinds.

Number of partitions of n into parts of 19 kinds.

Number of partitions of n into parts of 20 kinds.

Number of partitions of n into parts of 21 kinds.

Number of partitions of n into parts of 22 kinds.

Number of partitions of n into parts of 23 kinds.

Number of partitions of n into two relatively prime parts. After initial term, this is the "half-totient" function phi(n)/2 (A000010(n)/2).

Number of partitions of n into 3 unordered relatively prime parts.

Number of partitions of n into 4 unordered relatively prime parts.

Number of partitions of n into 5 unordered relatively prime parts.

Number of partitions of n into 6 unordered relatively prime parts.

Number of partitions of n into 7 unordered relatively prime parts.

Number of partitions of n into 8 unordered relatively prime parts.

Number of partitions of n into 9 unordered relatively prime parts.

Number of partitions of n into 10 unordered relatively prime parts.

Number of compositions of n into 6 ordered relatively prime parts.

Number of compositions of n into 7 ordered relatively prime parts.

Number of compositions of n into 8 ordered relatively prime parts.

Number of compositions of n into 9 ordered relatively prime parts.

Number of compositions of n into 10 ordered relatively prime parts.

Smallest positive even integer that is an unordered sum of two primes in exactly n ways.

a(n) = n^0 + n^1 + ... + n^(n-1), or a(n) = (n^n-1)/(n-1) with a(0)=0; a(1)=1.

a(n) = 12*a(n-1) - a(n-2).

a(n) = 18*a(n-1) - a(n-2).

w such that w^3+x^3+y^3+z^3=0, w>|x|>|y|>|z|, is soluble (all solutions).

w such that w^3 = x^3+y^3+z^3, x>y>z>=0, is soluble (primitive solutions).

Numbers whose cube is the sum of three distinct nonnegative cubes.

6th differences of factorial numbers.

7th differences of factorial numbers.

8th differences of factorial numbers.

9th differences of factorial numbers.

10th differences of factorial numbers.

Smallest prime having least positive primitive root n, or 0 if no such prime exists.

Smallest prime > n having primitive root n, or 0 if no such prime exists.

Sum of two coprime cubes in at least three ways.

Numbers that are the sum of two positive cubes in at least four ways (all solutions).

Perfect Digital Invariants: numbers that are the sum of some fixed power of their digits.

Number of noncrossing rooted trees with n nodes on a circle that do not have leaves at level 1.

Simon Plouffe's conjectured extension of sequence A008368.

(Apparently) differences between adjacent perfect powers (integers of form a^b, a >= 1, b >= 2).

a(n) is least k such that k and k+n are adjacent nontrivial powers of positive integers, or 0 if no such k apparently exists.

(Apparently) not the difference between adjacent perfect powers (A001597, integers of form a^b, a >= 1, b >= 2).

Positive numbers k such that k and 2*k are anagrams of each other in base 3 (k is written here in base 3).

Positive numbers k such that k and 2*k are anagrams in base 4 (written in base 4).

Positive numbers k such that k and 3*k are anagrams in base 4 (written in base 4).